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Quantum Mechanics for

Scientists and Engineers

David Miller

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Introduction to quantum mechanics

Lilght

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Black-body spectrum

Output power (per unit

wavelength)For a black body at 5800K

approximately like the sun

For a black body at 3000Kapproximately like anincandescent light bulb

Wavelength (nm)

500 1000 1500 2000

Power/unit

wavelength

(arbitra

ryunits)

0

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Black-body spectrum

Visible light spectrum

For a black body at 5800Kapproximately like the sun

For a black body at 3000K

approximately like anincandescent light bulb

Wavelength (nm)

500 600 700

Power/unit

wavelength

(arbitra

ryunits)

400

x 25

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Black-body spectrum

Output power (per unit

wavelength)For a black body at 5800K

approximately like the sun

The Rayleigh-Jeans classicalmodel gives theultra-violet catastrophe

showing no good

explanation for theshape of the curve Wavelength (nm)

500 1000 1500 2000

Power/unit

wavelength

(arbitra

ryunits)

0

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Light is emitted in quanta of

energy

where (Greek letter nu)

is the lights frequency inHz (Hertz) andh is Plancks constant

J s(Joule seconds)

Plancks proposal

E h

34

6.62606957 10h

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VI-+

Metal

plate

Light

Flow of

negativecharge

Collecting

plate

Photoelectric effect

Shining ultraviolet light on the

metal plategives flow of negative charge(Hertz, 1887)

Flow can be stopped with aspecific voltageindependent of thebrightness

but dependent only on thefrequency (Lenard, 1902)

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workfunction,

metal vacuum

electro

nenergy

pool of

electronsin metal

photonenergy,h

kinetic energy ofemitted electron

Photoelectric effect

Einsteins proposal (1905)

light is actually made up outof particlesphotons, of energy

The kinetic energy of theemitted electronsis the energy left over after

the electron has been

lifted over the workfunction barrier

E h

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Wave-particle duality

How can light simultaneously be

a wave and a particle?In the end, this is arguably not a problem for

quantum mechanics

we just need to avoid bringing along all theclassical attributes of particles and of wavesThe wave-particle duality of light is verified

trillions of times a day

in optical fiber communications

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Introduction to quantum mechanics

Matter

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H-alpha

656.3 nm

H-beta

486.1 nm

H-gamma

431.4 nm

H-delta

410.2 nm

Hydrogen atom emission spectra

Hot hydrogen emits lightin a set of spectral lines

Balmer seriesset of lines in the visible spectrum

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2

h

Bohr model of the hydrogen atom

A small negatively charged electronorbits a small positively charged

core (the proton)like a planet round a sun

but with electrostatic attractionKey assumption (Neils Bohr, 1913)

angular momentum is quantizedin units of Plancks constant, h,over 2

proton

electron

h bar

2n 1n

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2

h

Bohr model of the hydrogen atom

The model does give the photonenergies of the spectral linesas the separations of the

energies of the different orbits

proton

electron

h bar

1n 2n

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Hydro

genatome

nergy

n=2

n=3n=4

n=5n=6

H-alpha656.3 nm

n=3 ton=2

H-beta486.1 nm

n=4 ton=2

H-gamma431.4 nmn=5 to

n=2

H-delta410.2 nmn=6 to

n=2

Hydrogen atom emission spectra

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2

h

Bohr model of the hydrogen atom

The model

successfully introduces Plancksconstant into the theory ofmatter

gets the approximate size of theatom rightthe characteristic size is the

Bohr radius ~ 0.05 nm

0.5 (ngstrms)

proton

electron

h bar

1n 2n

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2

h

Bohr model of the hydrogen atom

The model does not get the angular

momentum quite rightthough the quantization inunits remains very important

It appears to predict the atom wouldradiate all the timefrom the orbiting electron

The atom does not look like this

it is not a small point electron ina classical orbit

proton

electron

h bar

1n 2n

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Hydrogen atom orbitals

4MM.3MM

n=1 n=2 l=1 m=1

Electron charge density in hydrogen orbitalsThe electron is not a moving point particle

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de Broglie hypothesis

A particle with mass

also behaves as a wavewith wavelength

wherep is the particlesmomentum

h

p

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Matrices and waves

Werner Heisenberg (1925)

matrix formulation ofquantum mechanics

Erwin Schrdinger (1926)wave equation

More key contributions byMax Born, Pascual Jordan,

Paul Dirac, John von

Neumann,

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Introduction to quantum mechanics

The usefulness of quantum mechanics

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Transistors and integrated circuits

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Transistors and gate tunneling

With smaller transistorsthe gate oxide becomes thinner

allowing quantum mechanical tunnelinggiving undesired gate leakage current

n+ n+

polysilicon

p

gate oxidechannel

GateSource Drain

silicon substrate

Tunneling current

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Introduction to quantum mechanics

Science, philosophy and meaning

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Reconstructing science

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What did you want to measure?

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Schrdingers cat

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More bizarre concepts

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Quantum mechanics works

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Using quantum mechanics

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