Physics 829
Dr. Herbst
Spring 2000
MIDTERM EXAMINATION (In Class; Closed Book)
12 MAY
(100 POINTS)
1) (20 points) A onedimensional harmonic oscillator is subjected to a
perturbation of the type ax3. Use stationary perturbation theory through second
order
Physics 829
Dr. Herbst
Spring 2001
MIDTERM EXAMINATION (In Class; Closed Book)
11 MAY
(100 POINTS)
(1) (30 points) Estimate the energy through firstorder of perturbation theory for
a hydrogen atom in its ground state with a finite spherical nucleus of ra
Physics 829
Dr. Herbst
Spring 2001
FINAL EXAMINATION (In Class; Closed Book)
4 JUNE
(150 POINTS)
1. (40 pts) In the theory of the interaction of radiation with matter, consider the
1 22
W =
q Az interaction term we neglected in class. Using the semiclassi
Physics 829
Dr. Herbst
Spring 2000
FINAL EXAMINATION (In Class; Closed Book)
5 JUNE
(150 POINTS)
1. (40 pts) In the theory of the interaction of radiation with matter, consider the
W = q/m PzAz interaction term. To solve the following problem, you may us
Physics 829
Dr. Herbst
Spring 2001
Homework Assignment # 1
Due: 6 April 2001
1) CT, Complement HXI , p. 1200. Problems 1a, 2, 4b,d,e, 8a,b
2) Find, to firstorder, the changes in the energy levels of a hydrogen atom
produced by a unit increase of the nucl
Physics 829
Dr. Herbst
Spring 2001
Homework Assignment # 2
Due: 13 April 2001
1) CT, Complement HXI , p. 1200. Problems 8c, 9
2) Use the variational method to estimate the energy of the first excited state of
the onedimensional harmonic oscillator. Justi
Physics 829
Dr. Herbst
Spring 2001
Homework Assignment # 3
Due: 20 April 2001
1) An electron exists in its ground state in a onedimensional box (0xa) with
infinite walls. At t=, a homogeneous electric field E in the xdirection is turned
on according to
Physics 829
Dr. Herbst
Spring 2001
Homework Assignment # 4
Due: 27 April 2001
1) Consider an electron bound in the ground state of a onedimensional box
(a/2xa/2) of finite height V0. Assume that the ground state can be
represented by a particle in a box
Physics 829
Dr. Herbst
Spring 2001
Homework Assignment # 5
Due: 4 May 2001
1) Use the WKB method to determine the transmission coefficient for tunneling
by a particle of mass m under a onedimensional potential barrier of the type:
2
V(x) = V0(1  x /x02)
Physics 829
Dr. Herbst
Spring 2001
Homework Assignment # 6
Due: 18 May 2001
1) Assuming that the perturbation between electromagnetic radiation and matter
in the semiclassical treatment is given by WDE (t) for the polarized radiation
studied in class, de
Physics 829
Dr. Herbst
Spring 2001
Homework Assignment # 7
NOT TO BE GRADED
ANSWERS TO BE POSTED ON WEB SITE
1) Assuming no other degrees of freedom, find the allowed state vectors of a
system of two spin3/2 particles that are simultaneous eigenvectors o
SOME BASIC EQUATIONS
H = T + V = P 2 / 2M + V ( R)
>

>= ih
H
=
H
t
 u >< u = 1
i
d
i
i
Px =
><
h
ix


>= E 
><
X = ih
>
=1
px
[ J x , J y ] = i hJz
J 2  jm >= j ( j + 1)h2  jm >
J z  jm >= mh  jm >
m = j, j 1, j 2,., j
h
i
J = J x iJ y
Lz
SOME BASIC EQUATIONS
H = T + V = P 2 / 2M + V ( R)
>

>= ih
H
=
H
t
 u >< u = 1
i
d
i
i
Px =
><
h
ix


>= E 
><
X = ih
>
=1
px
[ J x , J y ] = i hJz
J 2  jm >= j ( j + 1)h2  jm >
J z  jm >= mh  jm >
m = j, j 1, j 2,., j
h
i
J = J x iJ y
Lz