quantum theory ii.ppt
TRANSCRIPT
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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
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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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Quantum Theory
Tunneling Microscope
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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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