Ph125a Homework Assignment #1 with HMs solutions
Due 5:00pm on Tuesday, October 3, in the box outside 24 Bridge Annex
Remember that you must perform all calculations by hand and show your work for full
credit (see the course web page for details on the 3-
Ph125a HW #2 with HMs solutions
Due 5:00pm on Tuesday, October 10, in the box outside 24 Bridge Annex
Remember that you must perform all calculations by hand and show your work for full
credit (see the course web page for details on the 3-point grading sy
Ph125a, Fall 2012
Quantum Mechanics
Prof. Alexei Kitaev
Midterm
Due Tuesday, November 6, 2012
This midterm is, essentially, a non-collaboration homework. You may use the lecture notes
on the class web page, your own notes, and the books by Shankar and by
Ph125a, Fall 2012
Quantum Mechanics
Prof. Alexei Kitaev
Final exam
Due Friday, December 14, 2012
This nal is, essentially, a non-collaboration homework. You may use the lecture notes on
the class web page, your own notes, and the books by Shankar and by L
Solutions to the nal
Ph125a, Fall 2012
(Written by Alexei Kitaev)
1. Special evolution operators. The eigenfunctions and eigenvalues of the Hamiltonian are
as follows:
2
1
n2 .
(1)
n () = ein ,
En =
2mR2
2
Let us also calculate the evolution operator U (t
Ph125a HW#9 with HMs solutions
1. Spin rotation pulses
Suppose a spin- 1 degree of freedom with gyromagnetic ratio is subjected to a
2
constant magnetic field,
Bt b 1 z,
for a time interval
.
| |b 1
(a) Show that if the spin evolves according to the simp
Ph125a HW #8 with HMs solutions
1. More perturbation practice
Consider two spin- 1 degrees of freedom, whose joint pure states can be represented
2
by state vectors in the tensor-product Hilbert space
H AB H A H B ,
where H A and H B are each two-dimensio
Ph125a HW#7 with HMs solutions
1. Pauli matrices and the Bloch vector (a) Show that the Pauli operators, x 2 Sx, y 2 Sy, z 2 Sz, satisfy Tr i j 2 ij , where the indices i and j can take on the values x, y or z. You will probably want to work with matrix r
Ph125a HW#6 with HMs solutions
Due 5:00pm on Tuesday, 7 November, in the box outside 24 Bridge Annex
1. Eigenvalues of H and the range of H Suppose we specify a finite-dimensional Hilbert space H A and Hamiltonian operator H. Show that the states | H A wi
Ph125a HW #5 with HMs solutions
Due 5:00pm on Tuesday, 31 October, in the box outside 24 Bridge Annex
Remember that you must perform all calculations by hand and show your work for full
credit (see the course web page for details on the 3-point grading sy
Ph125a HW #4 with HMs solutions
Due 5:00pm on Tuesday, 24 October, in the box outside 24 Bridge Annex
Remember that you must perform all calculations by hand and show your work for full
credit (see the course web page for details on the 3-point grading sy
Ph125a HW #3 with HMs solutions
Due 5:00pm on Tuesday, 17 October, in the box outside 24 Bridge Annex
Remember that you must perform all calculations by hand and show your work for full
credit (see the course web page for details on the 3-point grading sy
Solutions to problem set 4
Ph125a, Fall 2012
(Written by Kevin Engel and Alexei Kitaev)
1. Generalized functions.
a)
f (x) =
eixy
dy
y
=
x
f (x) f () =
ieixy dy = 2i (x),
f (x) =
x
f (x)dx =
2i () dx = 2i (x),
x
where (x) is the Heaviside step function. W