Quantum Theory II.ppt

7/27/2019 Quantum Theory II.ppt

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Quantum Theory II

Schrdinger's Equation

Particle in a box or well

TunnelingHydrogen Atom

Spin


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Name That Tune

He was born on Sept 23, 1949

in Long Branch NJ

He is known for his brand of heartland rockinfused with pop hooks, poetic lyrics, and

Americana sentiments centered around his

native New Jersey.

His father was a bus driver

At the age of 13, he bought his first guitar for $18

after seeing Elvis Presley on the Ed Sullivan Show
http://images.google.com/imgres?imgurl=http://members.aol.com/daboss72/bruce/house1.jpg&imgrefurl=http://members.aol.com/daboss72/bruce/bruce.htm&h=400&w=600&sz=36&tbnid=JyjR9anCTLcQqM:&tbnh=88&tbnw=133&hl=en&start=76&prev=/images%3Fq%3DBruce%2BSpringsteen%26start%3D60%26svnum%3D10%26hl%3Den%26lr%3D%26sa%3DNhttp://images.google.com/imgres?imgurl=http://www.brucespringsteen.hu/images/kepek_nagy/2000_Bruce2002a.jpg&imgrefurl=http://www.brucespringsteen.hu/kepek_2000.htm&h=500&w=404&sz=45&tbnid=YIBZnneZ5fmofM:&tbnh=127&tbnw=102&hl=en&start=34&prev=/images%3Fq%3DBruce%2BSpringsteen%26start%3D20%26svnum%3D10%26hl%3Den%26lr%3D%26sa%3DN


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Name That Tune

He is known for his brand of heartland rockinfused with pop hooks, poetic lyrics, and

Americana sentiments centered around his

native New Jersey.

At the age of 13, he bought his first guitar for $18

after seeing Elvis Presley on the Ed Sullivan Show

He responded to the September 11, 2001

attacks was his album The Rising.

Frequently toured and recorded with E Street Band

He is probably best known for hisalbumBorn in the U.S.A.. (1984),

which sold 15 million copies.
http://en.wikipedia.org/wiki/Born_in_the_U.S.A.http://en.wikipedia.org/wiki/1984http://en.wikipedia.org/wiki/Born_in_the_U.S.A.http://en.wikipedia.org/wiki/1984http://en.wikipedia.org/wiki/1984http://en.wikipedia.org/wiki/Born_in_the_U.S.A.http://images.google.com/imgres?imgurl=http://images.art.com/images/-/Bruce-Springsteen--C10102050.jpeg&imgrefurl=http://www.art.com/asp/sp-asp/_/pd--10102050/Bruce_Springsteen.htm&h=477&w=385&sz=26&tbnid=sNiU4kuCVjg6gM:&tbnh=126&tbnw=101&hl=en&start=1&prev=/images%3Fq%3DBruce%2BSpringsteen%26svnum%3D10%26hl%3Den%26lr%3D%26sa%3DGhttp://images.google.com/imgres?imgurl=http://www.brucespringsteen.hu/images/kepek_nagy/2000_Bruce2002a.jpg&imgrefurl=http://www.brucespringsteen.hu/kepek_2000.htm&h=500&w=404&sz=45&tbnid=YIBZnneZ5fmofM:&tbnh=127&tbnw=102&hl=en&start=34&prev=/images%3Fq%3DBruce%2BSpringsteen%26start%3D20%26svnum%3D10%26hl%3Den%26lr%3D%26sa%3DN


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Quantum Theory II

Schrdinger's Equation

Particle in a box or well

TunnelingHydrogen Atom

Spin


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Schedule Change

Wednesday, April 26 Quantum Theory I

Read: Chapter 39

Friday, April 28 Quantum Theory II

Read: Chapter 40, Sections 1-4, 10Chapter 41, Sections 1-5

Monday, May 1 Exam #3

Wednesday, May 3 Nuclear Physics


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Class Question

This is the wave function of

a neutron. At what value ofx

is the neutron most likely to

be found?

1. x =xA

2. x =xB

3. x =xC

4. x = 0


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Class Question

This is the wave function of

a neutron. At what value ofx

is the neutron most likely to

be found?

1. x =xA

2. x =xB

3. x =xC

4. x = 0


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Reading Question

The quantity is called the

1. wave function.

2. probability.

3. probability density.4. amplitude density.

5. Schrdinger function.


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Reading Question

The quantity is called the

1. wave function.

2. probability.

3. probability density.4. amplitude density.

5. Schrdinger function.


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Quantum Theory

Matter Waves

hfE

khp


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Quantum Theory

This is one of the most important

equations in physics

),,(),,(),,(),,(2

2

2

zyxEzyxzyxVzyxm

),,(),,(),,( zyxEzyxVzyxK opop

EVK

),,(),,(),,( zyxzyxdVzyxP

?4 i 212

imaginary numbers

imaginary function


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Quantum Theory

Schrdinger's Equation in

One-dimension

)()()()(2 2

22xExxVx

dxd

m

)()()()(2

xxxdxxP

)(isequationthistosolutionThe x


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Quantum Theory

Below are the wave functions for two different particles.

Which particle has the largest momentum? Explain.

particle 1

particle 2

)(2

)(22

2

xmE

xdx

d

In one-dimension

and no potentialenergy

Kp2

2m

So matter wave with the largest curvature (smallest

wavelength) has the largest momentum.


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Quantum Theory

The wave function has no physical meaning, but dx

does. What is the physical meaning ofdx? Discuss

this in your group.

Below is a plot of for an electron in a electrical

potential. Where is the electron most likely to be found?

Explain.

(x)(x)dxThe largest probability iswhere the function is a

maximum.

Probability of finding the particle in dx


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Student Workbook


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Student Workbook


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Quantum Theory

)()(2 2

22

xExdx

d

m

)()(2)(22

2

xaxmExdxd

kxAx sin)(

kxBx cos)(

kxBkxAx cossin)(

Boundary conditions 00)0( Bx

Particle in a one-dimensional box

kxAx sin)(

x = 0 x = L


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Quantum Theory

kxAx sin)(

2

2

2

8n

mL

hE

n

)()(2 2

22

xExdx

d

m

nLk 22

0)(

Lx

Boundary condition

Particle in a one-dimensional box

x = 0 x = L


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Quantum Theory

dxxxdxxP )()()(

xkAx nsin)(

xkA

xxxP

n

22 sin

)()()(


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Quantum Theory

The Infinite Square Well or Particle in a Box What is the equation that describes the energy for a particle

in a box?

What is the ground state energy for an electron in a box 5.0nm in length?

What is the energy of the first excited state for an electronin a box 1.0 nm in length?

En 2h2

mL2n

2

eV

nmkgX

JsX

mL

hE ??

0.51011.9

106.621

2229

34

2

2

2

1

E2

E1

n2


24/43

Quantum Theory

Growth via Chemical Beam Epitaxy (CBE) A contacted InAs/InP nanowire

50nm

0.6 eV

InA

s

InA

s

InA

s

In

P

In

P

Ec

TEM photo of InAs/InP nanowire Energy landscape

TMInP2(As2)


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Student Workbook


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Student Workbook


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Student Workbook


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Student Workbook


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Student Workbook


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Class Question

A particle in the ground state of a potential energy well

1. is at rest.

2. has a zero-point motion.

3. is equally probable to be found at any pointinside the well.

4. has a wave function that is zero at all points.

5. has zero energy.


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Class Question

A particle in the ground state of a potential energy well

1. is at rest.

2. has a zero-point motion.

3. is equally probable to be found at any pointinside the well.

4. has a wave function that is zero at all points.

5. has zero energy.


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Class Question

A particle in a rigid box in the n = 2 stationary state is most

likely to be found

1. One-quarter of the way from either end.

2. One-third of the way from either end.3. In the center of the box.

4. It is equally likely to be found at any point

in the box.


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Class Question

A particle in a rigid box in the n = 2 stationary state is most

likely to be found

1. One-quarter of the way from either end.

2. One-third of the way from either end.3. In the center of the box.

4. It is equally likely to be found at any point

in the box.


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Class Question

For which potential energy is this an appropriate n = 4

wave function?

(1) (2) (3) (4)


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Quantum Theory

Plot the energy levels for a particle in a box (n = 1 to 5) andthe energy levels we found for the hydrogen atom (n = 1 to 4).

E = 0

E = -10 eV

E = -5 eV

E = 5 eV

E = 10 eV

E = 15 eV

E = -15 eV

n = 1

n = 2n = 3

n = infinityn = 1

n = 2

n = 3


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39/43

Quantum Theory

Tunneling Microscope


40/43

Student Workbook


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Class Question

A quantum particle can pass through a region of space that

would be forbidden to a classical particle. What is the name of

this process?1. Teleportation

2. Vacuum decay3. Lasing

4. Trapping

5. Tunneling


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Class Question

1. Decreases.

2. Increases.

3. Does not change.

A particle with energyEapproaches an energy barrier with

height U0 >E. IfU0 is slowly decreased, the probability that

the particle reflects from the barrier


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Quantum Theory II.ppt