Ph125b HW#8 with HMs solutions
(Cohen-Tannoudji, Diu, and Laloe, Complement G X Exercise 3.)
For the first two problems, consider a system of two spin 1/2 particles whose orbital
variables (position and momentum) are ignored. The Hamiltonian of the system
Ph125b HW#7 with HMs solutions
1. Groups of matrices [from Merzbacher]
Show that the three Pauli spin matrices, x , y , z , supplemented by the identity I do
not constitute a group under matrix mutliplication, but that if these matrices are
multiplied by
Ph125b HW#6 with HMs solutions
1. Wave-functions and orbital angular momentum
[modified from Merzbacher, Chapter 11, Problem #1]
Consider the state represented by the wave function,
2
x, y, z Ne r x y z.
(a) Determine the normalization constant N as a fun
Ph125b HW#5 with HMs solutions
1. Double-step potential [from Liboff]
Calculate the transmission coefficient (ratio of transmitted to incident probability
currents) for the double potential step,
V x 0
x 0,
V1
0 x a,
V2
x a,
where 0 V 1 V 2 . Assume tha
Ph125b HW#4 with HMs solutions
1. Harmonic oscillator eigenstates (Sakurai, Chapter 2, Problem 13)
Consider a one-dimensional simple harmonic oscillator. Using
ip
ip
a m x m , a m x m ,
2
2
a| n n | n 1 , a | n n 1 | n 1 ,
evaluate m | x | n , m | p | n ,
Ph125b HW#3 with HMs solutions
1. Zero-point energy
In class we discussed the fact that the ground state is forbidden from having zero
energy by the Uncertainty Principle. But at least classically, we know that we can shift
all energies in a problem by an
Ted Corcovilos (corcoted@caltech.edu) Physics 125b HW1 solutions
1
9 Jan. 2007
Continuity equation
Problem
Starting with the Schrdinger equation
o
i
h
h
2 2
(x, t) + V (x) (x, t),
(x, t) =
t
2m x2
(1)
where V (x) is an arbitrary real-valued function o