UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Physics
Physics 215B
Winter 2010
Prof. Gary Horowitz
TA Anthony Karmis
ASSIGNMENT #6
Due by Thursday, February 25 at 5pm
1) An electron is in a time-dependent magnetic eld B(t) = B0 + cos(t)+ sin(t) .
Physics 215A PS 6 Solutions
Anthony Karmis
March 4, 2010
Problem 1
An electron is in a time-dependent magnetic eld
B (t) = B0 [ + cos (t) x + sin (t) y]
z
The Hamiltonian is
e
1
S B (t) = c [ + cos (t) x + sin (t) y ]
h
z
mc
2
H (t) =
where c =
eB0
mc
is
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Physics
Physics 215B
Winter 2010
Prof. Gary Horowitz
TA Anthony Karmis
ASSIGNMENT #4
Due by Wednesday, February 10 at 5pm
1) Consider a (free) electron in a constant magnetic eld B = B and a perpendicu
Physics 215A PS 5 Solutions
Anthony Karmis
February 24, 2010
Problem 1
H
1 2 1
p + m 2 et x2
2m
2
1
1 2 1
p + m 2 x2 m 2 1 et x2
2m
2
2
H0 + V (t)
=
=
=
with:
H0
1 2
p +
2m
1
m 2
2
=
V (t) =
1
m 2 x2
2
1 et x2
Part (a)
From Sakurai Eq. 5.6.17, we see:
=
Physics 215A PS 4 Solutions
Anthony Karmis
February 15, 2010
Problem 1
If we have a particle interacting with an electromagnetic eld our hamiltonian
will be:
H=
1
2m
h
q
A
c
2
+ q
For an electron, q = e. Given a magnetic eld B = B z and electric eld
E =
Physics 215A PS 3 Solutions
Anthony Karmis
February 10, 2010
Problem 1
H=
h
2 2
1
px + p2 + m 2 x2 + y 2 + m 2 xy
y
2m
2
Part (a)
Treating the last term as a perturbation, we have:
1
h
2 2
p + p2 + m 2 x2 + y 2
y
2m x
2
which has solutions nx , ny with en
Physics 215A PS 1 Solutions
Anthony Karmis
January 20, 2010
Problem 1
Consider a three dimensional isotropic harmonic oscillator with frequency .
p2
1
H=
+ m 2 r2
2m 2
Part (a)
In Cartesian coordinates, we can use separation of variables to turn this into
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Physics
Physics 215B
Winter 2010
Prof. Gary Horowitz
TA Anthony Karmis
ASSIGNMENT #1
Due by Wednesday, January 13 at 5pm
1) Consider a three dimensional isotropic harmonic oscillator with frequency .
a
Physics 215A PS 2 Solutions
Anthony Karmis
February 2, 2010
Problem 1
V (x) =
1
m 2 x2 + x3
2
Part (a)
First we nd the rst correction to the energy,
(1)
En =< n(0) |V |n(0) >
where V is the perturbation potential, x3 .
To simplify things, we can relate x
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Physics
Physics 215B
Winter 2010
Prof. Gary Horowitz
TA Anthony Karmis
ASSIGNMENT #5
Due by Thursday, February 18 at 5pm
1) Consider a one-dimensional harmonic oscillator with a spring constant that sl
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Physics
Physics 215B
Winter 2010
Prof. Gary Horowitz
TA Anthony Karmis
ASSIGNMENT #2
Due by Wednesday, January 27 at 5pm
1) Consider a particle of mass m in one dimension with a potential V (x) given b