PHYS431 QUANTUM MECHANICS
HOMEWORK ASSIGNMENT #3
Due: Friday, March 22, 2013 (before 13:40)
Q1) Consider the motion of a particle of mass m in the potential
corresponding to a 3-dimensional harmonic oscillator.
(a) Separate the Shrdinger equation
in Carte
PHYS 431 QUANTUM MECHANICS
HOMEWORK ASSIGNMENT #5
Solutions
Q1)
a) Since =
11
) = is Hermitian
1 1
then is unitary. Then we have = = . Let us calculate this:
11 1 11 1
12 0
10
=
(
)
(
)= (
)=(
) =
01
20 2
2 1 1 2 1 1
1
2
1
b) If =
(
c) Tr()=0
d) To fin
PHYS 431
QUANTUM MECHANICS
HOMEWORK ASSIGNMENT #6
Due: Monday, May 13, 2013 (before 12:30)
(Solutions will be announced at 14:00)
2
( ). What is the probability that a measurement of the
1
= 1 (3 + 4 ) yields the value /2?
operator 5
Q1) Consider the spi
PHYS431 QUANTUM MECHANICS
HOMEWORK ASSIGNMENT #4
Due: Thursday, April 4, 2013 (before 17:30)
Q1) A particle of mass m is constrained to move between two concentric impermeable spheres
of radii
and
. There is no other potential, i.e.,
Show that ground stat
PHYS 431 QUANTUM MECHANICS
HOMEWORK ASSIGNMENT #5
Due: Friday, April 26, 2013 (before 17:30)
Q1) Consider the operator , which is represented by the matrix
a)
b)
c)
d)
Is Hermitian?
Is unitary?
Find Tr( )
Find the eigenvalues and eigenvectors of this matr
PHYS431 QUANTUM MECHANICS
HOMEWORK ASSIGNMENT #1
Due: Friday, March 8, 2013 (before 13:40)
Q1) Use problem 9.14 from the Liboffs book, to show that
and
Q2) Consider a molecule which may be represented by a dumbbell consisting of two equal
masses m attache
PHYS431 QUANTUM MECHANICS
HOMEWORK ASSIGNMENT #2
Due: Friday, March 15, 2013 (before 13:40)
Q1) Suppose that is measured for a rigid rotator and the value
is found.
(a) If
is then measured, what possible values can result? Why?
(b) Instead of , if one fir