PHYS 115B Homework 5 Solutions Spring 2008
Problem 1
(a) Recall the one dimensional harmonic oscillator n (x) = An Hn (x)e- In RECTANGULAR coordinates, separation of variables gives: = nx (x) ny (y) nz (z) = Anx Hnx (x) e-
2 x2 /2 2 x2 /2
, where
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A Review of Quantum Mechanics
Chun Wa Wong
Department of Physics and Astronomy, University of California, Los Angeles, CA 90095-1547
(Dated: September 21, 2006)
Review notes prepared for students of an undergraduate course in quantum mechanics at UCLA,
c
PHYS 115B Final Assignment
Page 1/1
Within 3-5 pages (handwritten or single-spaced typed), summarize the most important things to know
about the course. Specically, please discuss at least the following topics as well as what each has allowed us
to unders
Alexandre Streicher
Physics 115B Midterm Study Questions
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1. (Long! may want to do last) From nothing but Schrodingers equation and the appropriate potential, derive the spectrum of hydrogen. (you can do it! dont just convince
yourself that you co
Alexandre Streicher
Physics 115B Week 1&2 Study Questions
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1. Write down the 3d time-dependent Schrodinger equation
2. Derive the 3d time-independent Schrodinger equation
3. Given an initial wavefunction (x, y, z, 0), what does the Schrodinger equ
Alexandre Streicher
1.
211
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Week 4 Mastery Questions
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state of hydrogen
Write down the wave function describing the 211 state of hydrogen in terms of r and the Bohr radius a.
Find hri for the 211 state of hydrogen. (
Alexandre Streicher
Week 5 Mastery Questions
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Spinning Practice
1. When Griths says , is that a spinor, a spinor wavefunction, or a spin state?
2. What is a spin state?
3. What is a spinor?/What is a spin wavefunction? What is the basis?
4. Expres
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Jimmy Shen
PHYS 115A
Homework #7
November 24, 2013
2.37
Note that:
sin (3 ) = 3 sin 4 sin3
we have that:
3
1
x
x
= sin
sin
sin3
a
4
a
4
3x
a
since the eigen-states are given by: n ( x ) =
2
a
sin
n
a x
.
We can write
a 3
1
1 ( x ) 3 ( x )
2 4
4
( x, 0)
Jimmy Shen
PHYS 115A
Homework #8
December 3, 2013
2.41
(a)
Recall:
y0 =
y1 =
y2 =
mw 2
mw 1/4
h
e 2 x
p
h
1
mw 1/4
p
2mwxe
h
2 mw p
h
1
p
2
mw 1/4
p
h
2mw 2
h x
mw x2
2
h
1 e
mw x2
2
h
Keeping the relative amplitudes of the wave functions the same:
mw 2
h
PHYS 115A: Homework #3 Solution Set
Charlotte Mason
cmason@ucsb.physics.edu
Problem 1
Griths 2.3
Show that there is no acceptable solution to the time independent Schrdinger equation (TISE) for a particle in an innite square well with E = 0 or E < 0.
Foll
Jimmy Shen
PHYS 115A
Homework #2
October 10, 2013
Problem 1
(a)
If there was no current or charge
rE =
r
e0
rE =
rB = 0
B
t
0 e0 E
t
rB =
r2 a
Using: r r a = r (r a)
we get:
r (r E) = r (r E)
with the fact that 0 e0 =
r2 E =
1
c2
r2 E =
0 e0
(rB)
t
v2
c2
Jimmy Shen
PHYS 115A
Homework #4
November 6, 2013
2.18
Aeikx + Be
ikx
= A (cos kx + i sin kx ) + B (cos kx i sin kx )
= ( A + B) cos kx + i ( A B) sin kx
thus C = A + B and D = i ( A
B)
we can revert the relationship by solving the two equations above for
Jimmy Shen
PHYS 115A
Homework #4
October 23, 2013
Grifth 2.10
(a)
y0 =
mw 1/4
p
h
e
mw x2
2
h
Using the fact that a+ yn =
p
n + 1yn+1 we get y1 :
1
y1 = p a+ y0
1!
1
d
mw 1/4 mw x2
h
= p
h
+ mwx
e 2
dx
p
h
2 mw
h
mw
mw 1/4
1
= p
h
2x + mwx
e
2
h
p
h
2
PHYS 115A: Quantum Mechanics
Fall 2013
Homework #6 Solutions
TA: Charlotte Mason
cmason@physiscs.ucsb.edu
1. Griths 2.27
9 pts.
V (x) = [(x + a) + (x a)]
where and a are positive constants.
Solution:
(a) Sketch the potential:
v(x)
x
-a
a
Figure 1: Sketch
Alexandre Streicher
Week 6 Mastery Questions
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Spin Conceptual Practice
1. When Griths says , is that a spinor, a spinor wavefunction, or a spin state?
2. What is a spin state?
3. What is a spinor?/What is a spin wavefunction? What is the basis?
1