Graduate Quantum Mechanics I
PHY505
Homework 2 Due: Monday, 3/28/2016, to TA
Each problem is worth 15 points in this assignement.
1. In lectures we have developed a method to compute the propagator < x00 t | x0 0 >
for a free particle. Apply the method t
Graduate Quantum Mechanics I
PHY505
Homework 6 Due: Monday, 5/23/2016, to TA
Reading of the following weeks: Degenerate state perturbation theory (section
3.7(b), Time dependent perturbation theory (section 3.7(c) and (d), Variational
principle (section
Graduate Quantum Mechanics I
PHY505
Homework 5 Due: Monday, 5/9/2016, to TA
1. (a.) Let R1 and R2 be two infinitesimal rotations parametrized with 1 and
2 , and K a three-vector. If K is the change induced in K by R =
R21 R11 R2 R1 , show that to leading
Graduate Quantum Mechanics I
PHY505
Homework 7 Due: Wednesday, 6/1/2016, to TA
1. Estimate the ground state energy of a helium atom by the variational principle.
Use the hydrogen like wave functions as the trial functions and confirm the results
given in
Graduate Quantum Mechanics I
PHY505
Homework 4 Due: Friday, 4/15/2016, to TA
1. Problem 18, p. 239, Chapter 4, Gottfried & Yan. Assume the radii of the inner
and outer cylinders are a and b, respectively. Also assume the two ends of the
cylinder are at z
Graduate Quantum Mechanics I
PHY505
Homework 1 Due: Friday, 3/16/2016, to TA
1. (a)
Problem 2, p. 109, Chapter 2, Gottfried & Yan.
(b)
Show that U 1 f (A)U = f (U 1 AU ). Therefore, if U is unitary, the unitary
transform of the function of an operator A i
Physics 505 Final Exam - Solutions This final is a three hour open book, open notes exam. Do all four problems.
Fall 2007
[25 pts] 1. A point electric dipole with dipole moment p is located in vacuum pointing away from and a distance d away from the flat
Jackson 7.22 Homework Problem Solution
Dr. Christopher S. Baird
University of Massachusetts Lowell
PROBLEM:
Use the Kramers-Kronig relation to calculate the real part of (), given the imaginary part of () for
positive as
(a)
/ 0 =[ 1 2] , 2 > 1 > 0
(b)
/
Jackson 7.19 Homework Problem Solution
Dr. Christopher S. Baird
University of Massachusetts Lowell
PROBLEM:
An approximately monochromatic plane wave packet in one dimension has the instantaneous form,
u (x ,0)= f (x)e i k x , with f(x) the modulation env
Jackson 7.12 Homework Problem Solution
Dr. Christopher S. Baird
University of Massachusetts Lowell
PROBLEM:
The time dependence of electrical disturbances in good conductors is governed by the frequencydependent conductivity (7.58). Consider longitudinal
Jackson 7.3 Homework Problem Solution
Dr. Christopher S. Baird
University of Massachusetts Lowell
PROBLEM:
Two plane semi-infinite slabs of the same uniform, isotropic, nonpermeable, lossless dielectric with
index of refraction n are parallel and separate
Jackson 7.6 Homework Problem Solution
Dr. Christopher S. Baird
University of Massachusetts Lowell
PROBLEM:
A plane wave of frequency is incident normally from vacuum on a semi-infinite slab of material with
a complex index of refraction n() [n2() = ()/0].
Jackson 7.4 Homework Problem Solution
Dr. Christopher S. Baird
University of Massachusetts Lowell
PROBLEM:
A plane-polarized electromagnetic wave of frequency in free space is incident normally on the flat
surface of a non-permeable medium of conductivity
Jackson 7.1 Homework Problem Solution
Dr. Christopher S. Baird
University of Massachusetts Lowell
PROBLEM:
For each set of Stokes parameters given below deduce the amplitude of the electric field, up to an
overall phase, in both linear polarization and ci
Physics 505, Classical Electrodynamics
Homework 12
Due Friday, 10th December 2004
Jacob Lewis Bourjaily
Problem 7.28
Let us consider a circularly polarized plane wave moving in the z direction that has a nite extent
in the x and y directions. Assuming tha
Physics 505, Classical Electrodynamics
Homework 12
Due Friday, 10th December 2004
Jacob Lewis Bourjaily
Problem 7.28
Let us consider a circularly polarized plane wave moving in the z direction that has a nite extent
in the x and y directions. Assuming tha
2
JACOB LEWIS BOURJAILY
Problem 7.16
Let us consider plane waves propagating in a homogenous, nonpermeable but anisotropic dielectric.
The dielectric is characterized by the tensor ij . We will assume that the coordinate axes have been
chosen so that Di =
2
JACOB LEWIS BOURJAILY
Problem 7.16
Let us consider plane waves propagating in a homogenous, nonpermeable but anisotropic dielectric.
The dielectric is characterized by the tensor ij . We will assume that the coordinate axes have been
chosen so that Di =
Jackson 6.8 Homework Problem Solution
Dr. Christopher S. Baird
University of Massachusetts Lowell
PROBLEM:
A dielectric sphere of dielectric constant and radius a is located at the origin. There is a uniform
electric field E0 in the x direction. The spher
Jackson 6.9 Homework Problem Solution
Dr. Christopher S. Baird
University of Massachusetts Lowell
PROBLEM:
Discuss the conservation of energy and linear momentum for a macroscopic system of sources and
electromagnetic fields in a uniform, isotropic medium
Jackson 6.4 Homework Problem Solution
Dr. Christopher S. Baird
University of Massachusetts Lowell
PROBLEM:
A uniformly magnetized and conducting sphere of radius R and total magnetic moment m = 4MR3/3
rotates about its magnetization axis with angular spee
Jackson 6.1 Homework Problem Solution
Dr. Christopher S. Baird
University of Massachusetts Lowell
PROBLEM:
In three dimensions the solution to the wave equation (6.32) for a point source in space and time (a
light flash at t' = 0, x' = 0) is a spherical s
PHYSICS 505: CLASSICAL ELECTRODYNAMICS HOMEWORK 11
3
a) We are to apply a parity transformation on the monopole vector potential in problem (6.18)
above and determine its vector potential.
The magnetic eld, being a 2-form (or sheaf or pseudovector), is ev
Physics 505, Classical Electrodynamics
Homework 11
Due Tuesday, 30th November 2004
Jacob Lewis Bourjaily
Problem 6.15
Let us consider a conductor or semiconductor that has current induced by an applied electric eld
with an applied, transverse magnetic eld
Physics 505, Classical Electrodynamics
Homework 11
Due Tuesday, 30th November 2004
Jacob Lewis Bourjaily
Problem 6.15
Let us consider a conductor or semiconductor that has current induced by an applied electric eld
with an applied, transverse magnetic eld
4
JACOB LEWIS BOURJAILY
Problem 6.11
Let us consider a transverse plane wave that is normally incident in vacuum on a perfectly absorbing
at screen.
a) From the conservation of linear momentum, we are to show that the pressure exerted on the
screen is equ
PHYSICS 505: CLASSICAL ELECTRODYNAMICS HOMEWORK 10
3
Problem 6.9
We are to discuss the conservation of energy and linear momentum for a macroscopic system of sources
and electromagnetic elds in a uniform, isotropic medium described by a permittivity and a