Physics 517
Homework Set #1
Due in class 10/8/13
Autumn 2013
300 pts
1. (150 pts) Variations on Sakurai, 1.2, 1.9 and 1.11.:
a. Suppose a 2x2 matrix X is written as
X = a0 + a
where
1 =
0
1
1
0
,
2 =
Physics 518
Homework Set #7
Winter 2014
Due in class 3/5/14
300 pts
1. (75 pts) Factoring out the center of mass motion: Denote the coordinate
and momentum operators two particles interacting via a po
Physics 517
Homework Set #5
Autumn 2012
Due in class 11/6/12
300 pts
1. (60 pts) Sakurai, 2.7: Consider a free-particle wave packet in one dimension. At t = 0 it satises the mimimum uncertainty relati
Physics 517
Homework Set #6
Due in class 11/19/13
Autumn 2013
300 pts
1. (50 pts) Sakurai, 2.12.
a. Write down the wave function (in coordinate space) for the state formally
given by
ipa
|0
exp
h
wher
Physics 517
Homework Set #5
Due in class 11/12/13
Autumn 2013
300 pts
1. (75 pts) SHO via Shooting Method: We want to numerically nd the
eigenvalues of the SHO Hamiltonian by solving
x2
+ = E
2
2
(1)
Physics 517
Homework Set #7
Autumn 2013
Due in class 12/3/13
(Note that this is after the Thanksgiving break!)
300 pts
1. (100 pts) SUSY QM: Consider a 1d Schrdinger equation
o
1
+ V (x) = E
2
with p
Physics 517
Homework Set #6
Autumn 2013
Due in class 11/19/13
300 pts
1. (50 pts) Sakurai, 2.12;
a. Write down the wave function (in coordinate space) for the state formally
given by
ipa
|0
exp
h
wher
Physics 517
Homework Set #5
Due in class 11/12/13
Autumn 2013
300 pts
1. (75 pts) SHO via Shooting Method: We want to numerically nd the
eigenvalues of the SHO Hamiltonian by solving
x2
+ = E
2
2
(1)
Physics 517
Homework Set #7
Due in class 12/3/13
Autumn 2013
(Note that this is after the Thanksgiving break!)
300 pts
1. (100 pts) SUSY QM: Consider a 1d Schrdinger equation
o
1
+ V (x) = E
2
with p
Physics 518
Homework Set #6
Winter 2014
Due in class 2/26/14
300 pts
1. (75 pts) Sakurai, 3.20: We are to add angular momenta j1 = 1 and j2 = 1
to form j = 2, 1, and 0 states. Using either the ladder
Physics 518
Homework Set #5
Winter 2014
Due in class 2/19/14
300 pts
1. (50 pts) Variation on Sakurai, 3.4: Consider a spin 1 particle. Evaluate
the matrix elements of
Sz (Sz + )(Sz )
h
h
and
Sx (Sx +
Physics 517
Homework Set #1
Due in class 10/8/13
Autumn 2013
300 pts
1. (150 pts) Variations on Sakurai, 1.2, 1.9 and 1.11.:
a. Suppose a 2x2 matrix X is written as
X = a0 + a
where
1 =
0
1
1
0
,
2 =
Physics 518
Homework Set #4
Due in class 2/12/14
Winter 2014
300 pts
1. (100 pts) Derive an explicit form for the general rotation matrix
Rn () = exp(i T ) ,
n
where n is a unit vector giving the axis
Physics 517
Homework Set #3
Due in class 10/22/13
Autumn 2013
300 pts
1. (70 pts) Delta functions live under integral signs, and two expressions
D1 (x) and D2 (x) involving delta functiosn are said to
Physics 517
Homework Set #3
Autumn 2013
Due in class 10/22/13
300 pts
1. (70 pts) Delta functions live under integral signs, and two expressions
D1 (x) and D2 (x) involving delta functiosn are said to
Physics 517
Homework Set #4
Autumn 2013
Due in class 11/5/13
300 pts
1. (60 pts) Sakurai, 2.7: Consider a free-particle wave packet in one dimension. At t = 0 it satises the mimimum uncertainty relati
Physics 517
Homework Set #2
Due in class 10/15/13
Autumn 2013
300 pts
1. (60 pts) Derivation of Schwarz inequality (Sakurai, 1.18 a and b):
a. First argue that
( | + |) (| + | ) 0
for any complex numb
Physics 518
Homework Set #6
Due in class 2/26/14
Winter 2014
300 pts
1. (75 pts) Sakurai, 3.20: We are to add angular momenta j1 = 1 and j2 = 1
to form j = 2, 1, and 0 states. Using either the ladder
Physics 518
Homework Set #5
Due in class 2/19/14
Winter 2014
300 pts
1. (50 pts) Sakurai, 3.4: Consider a spin 1 particle. Evaluate the matrix
elements of
Sz (Sz + )(Sz )
h
h
and
Sx (Sx + )(Sx ).
h
h
Physics 518
Homework Set #7
Due in class 3/5/14
Winter 2014
300 pts
1. (75 pts) Factoring out the center of mass motion: Denote the coordinate
and momentum operators two particles interacting via a po
Physics 517
Homework Set #2
Due in class 10/15/13
Autumn 2013
300 pts
1. (60 pts) Derivation of Schwarz inequality (Sakurai, 1.18 a and b):
a. First argue that
( | + |) (| + | ) 0
for any complex numb