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TERM PAPER 

ON

“Wave function and wave equation; Electromagnetic wave; sound wave”

For 

Modern Physics and Electronics

Submitted To: Submitted By:

Lr. Sarita Devi Sharma

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Contents

• 1 Mathematical terminology

• 2 History and context

• 3 The Schrödinger equationo 3 .1 General quantum system

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o 3 .2 Single particle in three dimensions

• 4 Historical background and development

• 5 Derivation

o 6 .1 Short heuristic derivation

6.1 Assumptions

6.2 Expressing the wave function as a complex planewave

• 7 Versions

o 7 .1 Time dependent equation

o 7 .2 Time independent equation

• 8 Properties

o 8 .1 First order in time

o 8 .2 Linear 

o 8 .3 Real eigenstates

o 8 .4 Unitary time evolution

o 8.5 Correspondence principle

• 9 Relativity

• 10 Solutions

• 1 1 Range of the spectrum

• 12 Rationale

• 13 Types of radiation 

o 13.1 Radio frequency

o 13.2 Microwaves 

13.2.1 Terahertz radiation

o 13.3 Infrared radiation

o 13.4 Visible radiation (light)o 13.5 Ultraviolet light

o 13.6 X-rays

o 13.7 Gamma rays

Wave function

In quantum mechanics, wave function collapse (also called collapse of the state

vector or reduction of the wave packet) is the process by which a  wave function, 

initially in a superposition of different eigenstates, appears to reduce to a single one of 

the states after interaction with the external world. It is one of two processes by which

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quantum systems evolve in time according to the laws of  quantum mechanics as

 presented by John von Neumann.[1] The reality of wave function collapse has always

 been debated, i.e., whether it is a fundamental physical phenomenon in its own right

or just an epiphenomenon of another process, such as quantum decoherence. In recent

decades the quantum decoherence view has gained popularity.

•

Mathematical terminology

The state, or  wave function, of a physical system at some time can be expressed in

Dirac or  bra-ket notation as:

where the s specify the different quantum "alternatives" available (technically, they

form an orthonormal  eigenvector   basis, which implies ). An observable or 

measurable parameter of the system is associated with each eigenbasis, with each

quantum alternative having a specific value or eigenvalue, ei, of the observable.

The are the probability amplitude coefficients, which are complex numbers. 

For simplicity we shall assume that our wave function is normalised: , which

implies that

With these definitions it is easy to describe the process of collapse: when an external

agency measures the observable associated with the eigenbasis then the state of the

wave function changes from to just one of the s with Born probability  . This

is called collapse because all the other terms in the expansion of the wave function

have vanished or collapsed into nothing. If a more general measurement is made to

detect if the system is in a state then the system makes a "jump" or  quantum leap 

from the original state to the final state with probability of . Quantum

leaps and wave function collapse are therefore opposite sides of the same coin.

History and context

By the time  John von Neumann wrote his treatise Mathematische Grundlagen der Quantenmechanik  in 1932,[2] the phenomenon of "wave function collapse" was

accommodated into the  mathematical formulation of quantum mechanics by

 postulating that there were two processes of wave function change:

1. The   probabilistic, non-unitary, non-local, discontinuous change

 brought about by observation and measurement, as outlined above.

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2. The deterministic, unitary, continuous time evolution of an isolated

system that obeys Schrödinger's equation (or nowadays some relativistic, local 

equivalent).

In general, quantum systems exist in superpositions of those basis states that most

closely correspond to classical descriptions, and -- when not being measured or observed, evolve according to the time dependent  Schrödinger equation, relativistic

quantum field theory or some form of  quantum gravity or  string theory, which is

 process (2) mentioned above. However, when the wave function collapses -- process

(1) -- from an observer's perspective the state seems to "leap" or "jump" to just one of 

the basis states and uniquely acquire the value of the property being measured, ei, that

is associated with that particular basis state. After the collapse, the system begins to

evolve again according to the Schrödinger equation or some equivalent wave

equation.

By explicitly dealing with the interaction of object and measuring instrument von

 Neumann has attempted to prove consistency of the two processes (1) and (2) of wavefunction change.

He was able to prove the  possibility of a quantum mechanical measurement scheme

consistent with wave function collapse. However, he did not prove necessity of such a

collapse. Although von Neumann's projection postulate is often presented as a

normative description of quantum measurement it should be realized that it was

conceived by taking into account experimental evidence available during the 1930s

(in particular the Compton-Simon experiment has been paradigmatic), and that many

important    present-day measurement procedures do not satisfy it (socalled

measurements of the second kind).

The existence of the wave function collapse is required in

• the Copenhagen interpretation

• the objective collapse interpretations

• the so-called transactional interpretation

• in a "spiritual interpretation" in which consciousness causes collapse.

On the other hand, the collapse is considered as redundant or just an optional

approximation in

• interpretations based on consistent histories

• the many-worlds interpretation

• the Bohm interpretation

• the Ensemble Interpretation

The cluster of phenomena described by the expression wave function collapse is a

fundamental problem in the interpretation of quantum mechanics known as the

measurement problem. The problem is not really confronted by the Copenhagen

interpretation which simply postulates that this is a special characteristic of the

"measurement" process. The Everett many-worlds interpretation deals with it by

discarding the collapse-process, thus reformulating the relation between measurementapparatus and system in such a way that the linear laws of quantum mechanics are

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universally valid, that is, the only process according to which a quantum system

evolves is governed by the Schrödinger equation or some relativistic equivalent. Often

tied in with the many-worlds interpretation, but not limited to it, is the physical

  process of decoherence, which causes an apparent  collapse. Decoherence is also

important for the interpretation based on Consistent Histories.

 Note that a general description of the evolution of quantum mechanical systems is

 possible by using density operators and quantum operations. In this formalism (which

is closely related to the C*-algebraic formalism) the collapse of the wave function

corresponds to a non-unitary quantum operation.

 Note also that the physical significance ascribed to the wave function varies from

interpretation to interpretation, and even within an interpretation, such as the

Copenhagen Interpretation. If the wave function merely encodes an observer's

knowledge of the universe then the wave function collapse corresponds to the receipt

of new information -- this is somewhat analogous to the situation in classical physics,

except that the classical "wave function" does not necessarily obey a wave equation.If the wave function is physically real, in some sense and to some extent, then the

collapse of the wave function is also seen as a real process, to the same extent. One of 

the paradoxes of quantum theory is that wave function seems to be more than just

information (otherwise interference effects are hard to explain) and often less than

real, since the collapse seems to take place faster-than-light and triggered by

observers.

Schrodinger equation

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In physics, especially quantum mechanics, the Schrödinger equation is an equation

that describes how the quantum state  of a  physical system changes in time. It is as

central to quantum mechanics as  Newton's laws are to classical mechanics.

In the standard interpretation of quantum mechanics, the quantum state, also called a

wavefunction or state vector, is the most complete description that can be given to a physical system. Solutions to Schrödinger's equation describe atomic and subatomic

systems, electrons and atoms, but also macroscopic systems, possibly even the whole

universe. The equation is named after  Erwin Schrödinger , who discovered it in 1926.

Schrödinger's equation can be mathematically transformed into Heisenberg's matrix

mechanics, and into Feynman's  path integral formulation. The Schrödinger equation

describes time in a way that is inconvenient for relativistic theories, a problem which

is not as severe in Heisenberg's formulation and completely absent in the path

integral.

The Schrödinger equation takes several different forms, depending on the physicalsituation. This section presents the equation for the general case and for the simple

case encountered in many textbooks.

General quantum system

For a general quantum system:

where

• is the  wave function, which is the   probability

amplitude for different configurations of the system.

• is the Reduced Planck's constant, (Planck's constant divided

 by 2π), and it can be set to a value of 1 when using natural units.

• is the Hamiltonian operator .

Single particle in three dimensions

For a single particle in three dimensions:

where

• is the particle's position in three-dimensional

space,

• is the wavefunction, which is the amplitude for the particle to have a given position r at any given time t .

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• m is the mass of the particle.

• is the potential energy of the particle at each position r.

Historical background and development

Einstein interpreted Planck 's quanta as  photons, particles of light, and proposed that

the energy of a photon is proportional to its frequency, a mysterious wave-particle

duality. Since energy and momentum are related in the same way as frequency and

wavenumber in relativity, it followed that the momentum of a photon is proportional

to its wavenumber.

DeBroglie hypothesized that this is true for all particles, for electrons as well as

  photons, that the energy and momentum of an electron are the frequency and

wavenumber of a wave. Assuming that the waves travel roughly along classical paths,

he showed that they form standing waves only for certain discrete frequencies,

discrete energy levels which reproduced the old quantum condition.

Following up on these ideas, Schrödinger decided to find a proper wave equation for 

the electron. He was guided by Hamilton's analogy between mechanics and optics,

encoded in the observation that the zero-wavelength limit of optics resembles a

mechanical system--- the trajectories of light rays become sharp tracks which obey an

analog of the principle of least action. Hamilton believed that mechanics was the zero-

wavelength limit of wave propagation, but did not formulate an equation for those

waves. This is what Schrödinger did, and a modern version of his reasoning is

reproduced in the next section. The equation he found is (in natural units):

Using this equation, Schrödinger computed the spectral lines for hydrogen by

treating a hydrogen atom's single negatively charged  electron as a wave,

, moving in a  potential well,  V, created by the positively charged

 proton. This computation reproduced the energy levels of the Bohr model.

But this was not enough, since Sommerfeld had already seemingly correctly

reproduced relativistic corrections. Schrödinger used the relativistic energy

momentum relation to find what is now known as the Klein-Gordon equation in a

Coulomb potential:

He found the standing-waves of this relativistic equation, but the relativistic

corrections disagreed with Sommerfeld's formula. Discouraged, he put away his

calculations and secluded himself in an isolated mountain cabin with a lover 

While there, Schrödinger decided that the earlier nonrelativistic calculations were

novel enough to publish, and decided to leave off the problem of relativistic

corrections for the future. He put together his wave equation and the spectral analysis

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of hydrogen in a paper in 1926. The paper was enthusiastically endorsed by Einstein,

who saw the matter-waves as the visualizable antidote to what he considered to be the

overly formal matrix mechanics.

The Schrödinger equation tells you the behaviour of ψ, but does not say what ψ is.

Schrödinger tried unsuccessfully, in his fourth paper, to interpret it as a chargedensity. In 1926 Max Born, just a few days after Schrödinger's fourth and final paper 

was published, successfully interpreted ψ as a   probability amplitude. Schrödinger,

though, always opposed a  statistical or probabilistic approach, with its associated

discontinuities; like Einstein, who believed that quantum mechanics was a statistical

approximation to an underlying deterministic theory, Schrödinger was never 

reconciled to the Copenhagen interpretation.

Derivation

Short heuristic derivation

Assumptions

(1) The total energy  E of a particle is

This is the classical expression for a particle with mass m where the total

energy  E  is the sum of the kinetic energy, , and the   potential energy V .

The momentum of the particle is p, or mass times velocity. The potentialenergy is assumed to vary with position, and possibly time as well.

 Note that the energy E and momentum p appear in the following two relations:

(2) Einstein's light quanta hypothesis of 1905, which asserts that the energy E of a photon is proportional to the frequency  f  of the corresponding

electromagnetic wave:

where the  frequency  f  of the  quanta of radiation (photons) are related by

Planck's constant h,

and is the angular frequency of the wave.(3) The de Broglie hypothesis of 1924, which states that any particle can be

associated with a wave, represented mathematically by a wavefunction Ψ, and

that the momentum p of the particle is related to the wavelength λ of the

associated wave by:

where is the wavelength and is the wavenumber of the wave.

Expressing p and k as vectors, we have

Expressing the wave function as a complex plane wave

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Schrödinger's great insight, late in 1925, was to express the phase of a  plane wave as a

complex  phase factor :

and to realize that since

then

and similarly since

and

we find:

so that, again for a plane wave, he obtained:

And by inserting these expressions for the energy and momentum into the classical

formula we started with we get Schrödinger's famed equation for a single particle in

the 3-dimensional case in the presence of a potential V:

Versions

There are several equations which go by Schrödinger's name:

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Time dependent equation

This is the equation of motion for the quantum state. In the most general form, it is

written:

Where is a linear operator acting on the wavefunction Ψ. takes as input one Ψ

and produces another in a linear way, a function-space version of a matrix multiplying

a vector. For the specific case of a single particle in one dimension moving under the

influence of a potential V (adopting natural units where ):

and the operator H can be read off:

it is a combination of the operator which takes the second derivative, and the operator 

which pointwise multiplies Ψ by V(x). When acting on Ψ it reproduces the right hand

side.

For a particle in three dimensions, the only difference is more derivatives:

and for N particles, the difference is that the wavefunction is in 3N-dimensional

configuration space, the space of all possible particle positions.

This last equation is in a very high dimension, so that the solutions are not easy to

visualize.

Time independent equation

This is the equation for the standing waves, the eigenvalue equation for H. In abstract

form, for a general quantum system, it is written:

For a particle in one dimension,

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But there is a further restriction--- the solution must not grow at infinity, so that it has

a finite L^2-norm:

For example, when there is no potential, the equation reads:

which has oscillatory solutions for E>0 (the C's are arbitrary constants):

and exponential solutions for E<0

The exponentially growing solutions have an infinite norm, and are not physical. They

are not allowed in a finite volume with periodic or fixed boundary conditions.

For a constant potential V the solution is oscillatory for E>V and exponential for 

E<V, corresponding to energies which are allowed or disallowed in classical

mechnics. Oscillatory solutions have a classically allowed energy and correspond to

actual classical motions, while the exponential solutions have a disallowed energy and

describe a small amount of quantum bleeding into the classically disallowed region, to

quantum tunneling. If the potential V grows at infinity, the motion is classically

confined to a finite region, which means that in quantum mechanics every solution

 becomes an exponential far enough away. The condition that the exponential is

decreasing restricts the energy levels to a discrete set, called the allowed energies.

Properties

First order in time

The Schrödinger equation describes the time evolution of a quantum state, and must

determine the future value from the present value. A classical field equation can be

second order in time derivatives, the classical state can include the time derivative of 

the field. But a quantum state is a full description of a system, so that the Schrödinger 

equation is always first order in time.

Linear

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The Schrödinger equation is linear   in the wavefunction: if Ψ A( x,t ) and Ψ B( x,t ) are

solutions to the time dependent equation, then so is aΨ A + bΨ B, where a and b are any

complex numbers.

In quantum mechanics, the time evolution of a quantum state is always linear, for 

fundamental reasons. Although there are nonlinear versions of the Schrödinger equation, these are not equations which describe the evolution of a quantum state, but

classical field equations like Maxwell's equations or the Klein-Gordon equation.

The Schrödinger equation itself can be thought of as the equation of motion for a

classical field not for a wavefunction, and taking this point of view, it describes a

coherent wave of nonrelativistic matter, a wave of a Bose condensate or a  superfluid 

with a large indefinite number of particles and a definite phase and amplitude.

Real eigenstates

The time-independent equation is also linear, but in this case linearity has a slightly

different meaning. If two wavefunctions ψ1 and ψ2 are solutions to the time-

independent equation with the same energy  E , then any linear combination of the two

is a solution with energy  E . Two different solutions with the same energy are called

degenerate.

In an arbitrary potential, there is one obvious degeneracy: if a wavefunction ψ solves

the time-independent equation, so does ψ * . By taking linear combinations, the real

and imaginary part of ψ are each solutions. So that restricting attention to real valuedwavefunctions does not affect the time-independent eigenvalue problem.

In the time-dependent equation, complex conjugate waves move in opposite

directions. Given a solution to the time dependent equation , the

replacement:

 produces another solution, and is the extension of the complex conjugation symmetry

to the time-dependent case. The symmetry of complex conjugation is called time-reversal.

Unitary time evolution

The Schrödinger equation is Unitary, which means that the total norm of the

wavefunction, the sum of the squares of the value at all points:

has zero time derivative.

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The derivative of is according to the complex conjugate equations

where the operator is defined as the continuous analog of the Hermitian conjugate,

For a discrete basis, this just means that the matrix elements of the linear operator H

obey:

The derivative of the inner product is:

and is proportional to the imaginary part of H. If H has no imaginary part, if it is self-

adjoint, then the probability is conserved. This is true not just for the Schrödinger 

equation as written, but for the Schrödinger equation with nonlocal hopping:

so long as:

the particular choice:

reproduces the local hopping in the ordinary Schrödinger equation. On a discrete

lattice approximation to a continuous space, H(x,y) has a simple form:

whenever x and y are nearest neighbors. On the diagonal

where n is the number of nearest neighbors.

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Correspondence principle

The Schrödinger equation satisfies the correspondence principle. In the limit of small

wavelength wavepackets, it reproduces Newton's laws. This is easy to see from the

equivalence to matrix mechanics.

All operators in Heisenberg's formalism obey the quantum analog of Hamilton's

equations:

So that in particular, the equations of motion for the X and P operators are:

in the Schrödinger picture, the interpretation of this equation is that it gives the time

rate of change of the matrix element between two states when the states change with

time. Taking the expectation value in any state shows that Newton's laws hold not

only on average, but exactly, for the quantities:

Relativity

The Schrödinger equation does not take into account relativistic effects, as a wave

equation, it is invariant under a Galilean transformation, but not under a Lorentz

transformation. But in order to include relativity, the physical picture must be altered

in a radical way.

The Klein–Gordon equation uses the relativistic mass-energy relation (in natural

units):

to produce the differential equation:

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which is relativistically invariant, but second order in ψ, and so cannot be an equation

for the quantum state. This equation also has the property that there are solutions with

 both positive and negative frequency, a plane wave solution obeys:

which has two solutions, one with positive frequency the other with negative

frequency. This is a disaster for quantum mechanics, because it means that the energy

is unbounded below.

A more sophisticated attempt to solve this problem uses a first order wave equation,

the Dirac equation, but again there are negative energy solutions. In order to solve this

 problem, it is essential to go to a multiparticle picture, and to consider the wave

equations as equations of motion for a quantum field, not for a wavefunction.

The reason is that relativity is incompatible with a single particle picture. A

relativistic particle cannot be localized to a small region without the particle number  becoming indefinite. When a particle is localized in a box of length L, the momentum

is uncertain by an amount roughly proportional to h/L by the uncertainty principle. 

This leads to an energy uncertainty of hc/L, when |p| is large enough so that the mass

of the particle can be neglected. This uncertainty in energy is equal to the mass-

energy of the particle when

and this is called the Compton wavelength. Below this length, it is impossible tolocalize a particle and be sure that it stays a single particle, since the energy

uncertainty is large enough to produce more particles from the vacuum by the same

mechanism that localizes the original particle.

But there is another approach to relativistic quantum mechanics which does allow you

to follow single particle paths, and it was discovered within the  path-integral

formulation. If the integration paths in the path integral include paths which move

 both backwards and forwards in time as a function of their own proper time, it is

  possible to construct a purely positive frequency wavefunction for a relativistic

  particle. This construction is appealing, because the equation of motion for the

wavefunction is exactly the relativistic wave equation, but with a nonlocal constraintthat separates the positive and negative frequency solutions. The positive frequency

solutions travel forward in time, the negative frequency solutions travel backwards in

time. In this way, they both analytically continue to a statistical field correlation

function, which is also represented by a sum over paths. But in real space, they are the

 probability amplitudes for a particle to travel between two points, and can be used to

generate the interaction of particles in a point-splitting and joining framework. The

relativistic particle point of view is due to Richard Feynman.

Feynman's method also constructs the theory of quantized fields, but from a particle

 point of view. In this theory, the equations of motion for the field can be interpreted as

the equations of motion for a wavefunction only with caution--- the wavefunction isonly defined globally, and in some way related to the particle's proper time. The

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notion of a localized particle is also delicate--- a localized particle in the relativistic

 particle path integral corresponds to the state produced when a local field operator 

acts on the vacuum, and exacly which state is produced depends on the choice of field

variables.

Electromagnetic spectrum

Although some radiations are marked as  N for no in the diagram, some waves do in

fact penetrate the atmosphere, although extremely minimally compared to the other 

radiations

The electromagnetic (EM) spectrum is the range of all possible electromagneticradiation frequencies. The "electromagnetic spectrum" (usually just  spectrum) of an

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object is the characteristic distribution of electromagnetic radiation from that

 particular object.

The electromagnetic spectrum extends from below the frequencies used for modern

radio (at the long-wavelength end) through gamma radiation (at the short-wavelength

end), covering wavelengths from thousands of kilometers down to a fraction the sizeof an atom. It is thought that the short wavelength limit is in the vicinity of the Planck 

length, and the long wavelength limit is the size of the universe itself (see  physical

cosmology), although in principle the spectrum is infinite and continuous.

Range of the spectrum

EM waves are typically described by any of the following three physical properties:

the frequency,   f , and  wavelength, λ , and  photon  energy,  E . Frequencies range fromabout a million billion Hertz (gamma rays) down to a few Hertz (radio waves).

Wavelength is inversely proportional to the wave frequency, so gamma rays have

very short wavelengths that are fractions of the size of  atoms, whereas radio

wavelengths can be as long as several thousand kilometers. Photon energy is directly

 proportional to the wave frequency, so gamma rays have the highest energy around a

mega electron volt and radio waves have very low energy around femto electron volts

(femto = 10 − 15). These relations are illustrated by the following equations:

or or 

Where:

c = 299,792,458 m/s (speed of light in vacuum) and

h = 6.62606896(33)×10−34 J·s (Planck's constant).

Whenever light waves (and other electromagnetic waves) exist in a medium (matter),

their wavelength is decreased. Wavelengths of electromagnetic radiation, no matter 

what medium they are traveling through, are usually quoted in terms of the vacuum

wavelength , although this is not always explicitly stated.

Generally, EM radiation is classified by coiled  wavelength into radio wave, 

microwave,  infrared, the visible region we perceive as light, ultraviolet,  X-rays and

gamma rays.

The behavior of EM radiation depends on its wavelength. When EM radiation

interacts with single atoms and molecules, its behavior also depends on the amount of 

energy per quantum (photon) it carries. Electromagnetic radiation can be divided into

octaves — as sound waves are.

 Spectroscopy can detect a much wider region of the EM spectrum than the visible

range of 400 nm to 700 nm. A common laboratory spectroscope can detectwavelengths from 2 nm to 2500 nm. Detailed information about the physical

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 properties of objects, gases, or even stars can be obtained from this type of device. It

is widely used in astrophysics. For example, many hydrogen atoms emit a radio wave 

 photon which has a wavelength of 21.12 cm. Also, frequencies of 30 Hz and below

can be produced by and are important in the study of certain stellar nebulae and

frequencies as high as 2.9×1027 Hz have been detected from astrophysical sources.

Rationale

Electromagnetic radiation interacts with matter in different ways in different parts of 

the spectrum. The types of interaction can be so different that it seems to be justified

to refer to different types of radiation. At the same time there is a continuum

containing all these "different kinds" of electromagnetic radiation. Thus we refer to a

spectrum, but divide it up based on the different interactions with matter.

Region of the

spectrum

Main interactions with matter

RadioCollective oscillation of charge carriers in bulk material (plasma

oscillation). An antenna is an example.

Microwave

through far  

infrared

Plasma oscillation, molecular rotation

 Near infrared Molecular vibration, plasma oscillation (in metals only)

VisibleMolecular electron excitation (including pigment molecules found

in the human retina), plasma oscillations (in metals only)

UltravioletExcitation of molecular and atomic valence electrons, including

ejection of the electrons ( photoelectric effect)X-rays Excitation and ejection of core atomic electrons

Gamma raysEnergetic ejection of core electrons in heavy elements, excitation

of atomic nuclei, including dissociation of nuclei

High energy

gamma rays

Creation of particle-antiparticle pairs. At very high energies a

single photon can create a shower of high energy particles and

antiparticles upon interaction with matter.

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Types of radiation

The electromagnetic spectrum

While the classification scheme is generally accurate, in reality there is often some

overlap between neighboring types of electromagnetic energy. For example, SLFradio waves at 60 Hz may be received and studied by astronomers, or may be ducted

along wires as electric power.

The distinction between X and gamma rays is based on sources. "Gamma ray" is the

name given to the photons generated from nuclear decay  or other nuclear and

subnuclear/particle processes, whereas X-rays on the other hand are generated by

electronic  transitions involving highly energetic inner atomic electrons. Generally,

nuclear transitions are much more energetic than electronic transitions, so usually,

gamma-rays are more energetic than X-rays, but exceptions exist. By analogy to

electronic transitions,  muonic atom transitions are also said to produce X-rays, even

though their energy may exceed 6 MeV [8], whereas there are a few low-energy

nuclear transitions (e.g. the 14.4 keV nuclear transition of Fe-57), and despite being

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over 400-fold less energetic than some muonic X-rays, the emitted photons are still

called gamma rays due to their nuclear origin. [9]

Also, the region of the spectrum of particular electromagnetic radiation is reference-

frame dependent (on account of the Doppler shift for light) so EM radiation which

one observer would say is in one region of the spectrum could appear to an observer moving at a substantial fraction of the speed of light with respect to the first to be in

another part of the spectrum. For example, consider the cosmic microwave

 background. It was produced, when matter and radiation decoupled, by the de-

excitation of hydrogen atoms to the ground state. These photons were from Lyman

series  transitions, putting them in the ultraviolet (UV) part of the electromagnetic

spectrum. Now this radiation has undergone enough cosmological red shift  to put it

into the microwave region of the spectrum for observers moving slowly (compared to

the speed of light) with respect to the cosmos. However, for particles moving near the

speed of light, this radiation will be  blue-shifted in their rest frame. The highest

energy cosmic ray protons are moving such that, in their rest frame, this radiation is

 blueshifted to high energy gamma rays which interact with the proton to produce bound quark-antiquark pairs ( pions). This is the source of the GZK limit.

Radio frequency

Radio waves generally are utilized by antennas of appropriate size (according to the

 principle of resonance), with wavelengths ranging from hundreds of meters to about

one millimeter. They are used for transmission of data, via  modulation.  Television, 

mobile phones, wireless networking and amateur radio all use radio waves.

Radio waves can be made to carry information by varying a combination of theamplitude, frequency and phase of the wave within a frequency band and the use of 

the radio spectrum is regulated by many governments through frequency allocation. 

When EM radiation impinges upon a conductor , it couples to the conductor, travels

along it, and induces an electric current on the surface of that conductor by exciting

the electrons of the conducting material. This effect (the skin effect) is used in

antennas. EM radiation may also cause certain molecules to absorb energy and thus to

heat up, thus causing thermal effects and sometimes burns; this is exploited in

microwave ovens.

Microwaves

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Plot of Earth's atmospheric transmittance (or opacity) to various wavelengths of 

electromagnetic radiation.

The super high frequency (SHF) and extremely high frequency (EHF) of microwaves 

come next up the frequency scale. Microwaves are waves which are typically shortenough to employ tubular metal waveguides  of reasonable diameter. Microwave

energy is produced with klystron and magnetron  tubes, and with solid state diodes 

such as Gunn and IMPATT devices. Microwaves are absorbed by molecules that have

a dipole moment in liquids. In a microwave oven, this effect is used to heat food.

Low-intensity microwave radiation is used in Wi-Fi, although this is at intensity

levels unable to cause thermal heating.

Volumetric heating, as used by microwaves, transfer energy through the material

electro-magnetically, not as a thermal heat flux. The benefit of this is a more uniform

heating and reduced heating time; microwaves can heat material in less than 1% of the

time of conventional heating methods.

When active, the average microwave oven is powerful enough to cause interference at

close range with poorly shielded electromagnetic fields such as those found in mobile

medical devices and cheap consumer electronics.

Terahertz radiation

Terahertz radiation is a region of the spectrum between far infrared and microwaves.

Until recently, the range was rarely studied and few sources existed for microwave

energy at the high end of the band (sub-millimetre waves or so-called terahertz

waves), but applications such as imaging and communications are now appearing.

Scientists are also looking to apply terahertz technology in the armed forces, where

high frequency waves might be directed at enemy troops to incapacitate their 

electronic equipment.

Infrared radiation

The infrared  part of the electromagnetic spectrum covers the range from roughly 300

GHz (1 mm) to 400 THz (750 nm). It can be divided into three parts:

• Far-infrared, from 300 GHz (1 mm) to 30 THz (10 μm). The lower  part of this range may also be called microwaves. This radiation is typically

absorbed by so-called rotational modes in gas-phase molecules, by molecular 

motions in liquids, and by  phonons  in solids. The water in the Earth's

atmosphere absorbs so strongly in this range that it renders the atmosphere

effectively opaque. However, there are certain wavelength ranges ("windows")

within the opaque range which allow partial transmission, and can be used for 

astronomy. The wavelength range from approximately 200 μm up to a few

mm is often referred to as "sub-millimetre" in astronomy, reserving far 

infrared for wavelengths below 200 μm.

• Mid-infrared, from 30 to 120 THz (10 to 2.5 μm). Hot objects ( black-

 body radiators) can radiate strongly in this range. It is absorbed by molecular vibrations, where the different atoms in a molecule vibrate around their 

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equilibrium positions. This range is sometimes called the  fingerprint regionsince the mid-infrared absorption spectrum of a compound is very specific for 

that compound.

• Near-infrared, from 120 to 400 THz (2,500 to 750 nm). Physical

 processes that are relevant for this range are similar to those for visible light.

Visible radiation (light)

Visible Electromagnetic spectrum illustration.

The light spectrums of different grow lamps

Above infrared in frequency comes visible light. This is the range in which the  sun 

and stars similar to it emit most of their radiation. It is probably not a coincidence thatthe  human eye is sensitive to the wavelengths that the sun emits most strongly.

Visible light (and near-infrared light) is typically absorbed and emitted by electrons in

molecules and atoms that move from one energy level to another. The light we see

with our eyes is really a very small portion of the electromagnetic spectrum. A

rainbow shows the optical (visible) part of the electromagnetic spectrum; infrared (if 

you could see it) would be located just beyond the red side of the rainbow with

ultraviolet appearing just beyond the violet end.

EM radiation with a wavelength between 380  nm and 760 nm is detected by the

human eye and perceived as visible light. Other wavelengths, especially near infrared

(longer than 760 nm) and ultraviolet (shorter than 380 nm) are also sometimesreferred to as light, especially when the visibility to humans is not relevant.

If radiation having a frequency in the visible region of the EM spectrum reflects off of 

an object, say, a bowl of fruit, and then strikes our eyes, this results in our  visual

 perception of the scene. Our brain's visual system processes the multitude of reflected

frequencies into different shades and hues, and through this not-entirely-understood

 psychophysical phenomenon, most people perceive a bowl of fruit.

At most wavelengths, however, the information carried by electromagnetic radiation

is not directly detected by human senses. Natural sources produce EM radiation

across the spectrum, and our technology can also manipulate a broad range of wavelengths. Optical fiber  transmits light which, although not suitable for direct

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viewing, can carry data that can be translated into sound or an image. The coding used

in such data is similar to that used with radio waves.

Ultraviolet light

The amount of penetration of UV relative to altitude in Earth's ozone

 Next in frequency comes ultraviolet (UV). This is radiation whose wavelength is

shorter than the violet end of the visible spectrum, and longer than that of an x-ray.

Being very energetic, UV can break chemical bonds, making molecules unusually

reactive or ionizing them, in general changing their mutual behavior. Sunburn, for 

example, is caused by the disruptive effects of UV radiation on skin cells, which can

even cause skin cancer , if the radiation irreparably damages the complex DNA 

molecules in the cells (UV radiation is a proven mutagen). The Sun emits a large

amount of UV radiation, which could quickly turn Earth into a barren desert;

however, most of it is absorbed by the atmosphere's ozone layer before reaching thesurface.

X-rays

After UV come X-rays. Hard X-rays have shorter wavelengths than soft X-rays. As

they can pass through most substances, X-rays can be used to 'see through' objects,

most notably bodies (in medicine), as well as for high-energy physics and astronomy.

 Neutron stars and accretion disks around black holes emit X-rays, which enable us to

study them. X-rays are given off by stars, and strongly by some types of nebulae.

Gamma rays

After hard X-rays come gamma rays, which were discovered by Paul Villard in 1900.

These are the most energetic  photons having no defined lower limit to their 

wavelength. They are useful to astronomers in the study of high energy objects or 

regions and find a use with physicists thanks to their penetrative ability and their 

 production from radioisotopes. The wavelength of gamma rays can be measured with

high accuracy by means of  Compton scattering.

  Note that there are no precisely defined boundaries between the bands of the

electromagnetic spectrum. Radiation of some types have a mixture of the properties of 

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those in two regions of the spectrum. For example, red light resembles infrared

radiation in that it can resonate some chemical bonds.