Physics 417 Intermediate Quantum Mechanics
Midterm Exam Date: 10/24/2012 There are 4 problems. Do all of them. Show all your work. Cross things out neatly, DO NOT ERASE. This is a closed textbook exam
Physics 417
Intermediate Quantum Mechanics
Final Exam
Date: 12/21/2011
There are 6 problems. Do all of them. Show all your work. Cross things
out neatly, DO NOT ERASE.
This is a closed textbook exam.
Physics 417
Spring 2016
Homework 9
1) a) Determine the density matrix for the singlet state of a two electron system
1
| i | i
2
Note that since you are finding the density matrix for the full two e
Physics 417
Midterm Exam
March 11, 2015
The exam is 80 minutes in length.
There are four problems. All are worth the same amount of points.
00
You may refer to a single note sheet on 8 12 1100 paper (
Intermediate Quantum Mechanics
Spring 2016
Solutions Homework 6
1) Using a similar calculation to what I did in class to show that a
|En i is an energy eigenstate
with energy En + h
, show that a
|E
Intermediate Quantum Mechanics
Spring 2016
Solutions to Homework 7
1) Calculate the following commutators:
x, L
y]
[L
+, L
z]
[L
z]
[L2 , L
, L
z]
[L
+, L
]
[L
Solution
x = ypz zpy
L
y = zpx xp
Intermediate Quantum Mechanics
Spring 2016
Solutions to Homework 3
1) As we saw in class, the Dirac delta function can be defined as the limit of:
(x) = lim
N
1 sin(N x)
x
From this, use the Euler Re
Intermediate Quantum Mechanics
Spring 2016
Solutions to Homework 2
1) Prove that the trace of an operator, the sum of the diagonal elements of the matrix,
is independent of the basis chosen to represe
Intermediate Quantum Mechanics
Spring 2016
Homework 4
are Hermitian operators, then i times their commutator i[A,
B]
is
1) Show that if A and B
Hermitian.
Solution
B]
=
[A,
B
A = B
A A B
= B
Physics 417
Practice Midterm Exam Solutions
Problem 1
1
m 2 x2
2
1
At time t = 0, the particle is in the state: |(0)i = |E0 i + 2 |E1 i where |E0 i
3
and |E1 i are the ground and first excited energy
Intermediate Quantum Mechanics
Spring 2016
Solutions Homework 8
1) In class we discussed expressions for the ground state energy and the Bohr radius of the
hydrogen atom in terms of the constants: h
Physics 417
Solutions to Midterm Exam
spring 2016
Problem 1
a) An electron has a probability of 3/4 to be in the state with spin-up in the z-direction
and has a probability of 1/4 to be in the state w
Physics 417
Final Exam
May 11, 2015
The exam is 3 hours in length.
There are six problems. All are worth the same amount of points.
00
You may refer to two note sheets on 8 12 1100 paper (double-sided
Physics 417
Solutions to Practice Final Exam
Spring 2016
Problem 1
A particle is in the n = 2 excited state of a simple harmonic oscillator potential. In what
follows you may set m, ~ and all equal to
Physics 417
Intermediate Quantum Mechanics
Final Exam
Date: 12/19/2012
There are 6 problems. Do all of them. Show all your work. Cross things
out neatly, DO NOT ERASE.
This is a closed textbook exam.
Physics 417 Intermediate Quantum Mechanics
Midterm Exam Date: 10/26/2011 There are 4 problems. Do all of them. Show all your work. Cross things out neatly, DO NOT ERASE. This is a closed textbook exam