** Assignment
#1** Due
Mon, Aug 29

Chapter 2: Question 8, Question 22*

** Assignment
#2** Due Wed, Sep 7

Chapter 2: Question 13, 20, 23,

*Also calculate the spacetime interval. What type of interval is it?

**Cross off "at rest" :P

*** Assume these are super-vans and v is a substantial fraction of c.

Additional question #1: Use the fact that s^{2} is invariant, prove that no observer will see two events at the same place, if the spacetime interval is spacelike.

Additional question #2: GPS systems must correct for relativistic effects in order to get the tremendous accuracy they have.

a) Suppose that a GPS satellite is travelling at about 4 km/s relative to someone on earth. Because of this relative motion, time dilation predicts that the satellite's clock and the reciever's clock will tick at slightly different rates. Find the fraction by which the two times differ (for example, if one time is 1.001 times the other, then they differ by one part in 1000).

b) Use equation 15.4 to see how general relativity affects the ticking of the two clocks. The satellite orbits at a radius of about 26,600 km and we orbit at a radius of about the radius of the Earth. Find the fraction by which the two rates differ (this time, if Delta-f/f is 0.001 then they differ by one part in 1000).

For comparison, the satellites' clocks are generally accurate to one part in 10^{12} in their own frame.

Assignment #3 Due Mon, Sep 19

Chapter 3: Question 26, Problems 18, 21 (also, what part of the em
spectrum is this?), 33, 34, 37, Chapter 5: Problem 13a (note:
with light, it's usually just called "energy" and "wavelength,"
and the terms "kinetic energy" and "deBroglie wavelength" are usually
reserved for stuff with mass.)

Additional problem: Use the wavefunction given in chapter 5, problem 48 to answer:

a) Which is larger, the probability density at x=L/2 or the probability density at x=L?

b) Which is larger, the probability density at x=L/4 or the probability density at x=3L/4?

Assignment #4 Due Mon, Sep 26

Chapter 5: Question 15, 17, Problems 16, 26, 42, 43, 48, 64

Additional problem: Use the wavefunction given in chapter 5, problem 48 to answer:

a) What is the probability of finding the particle in the region L/4 < x < L/2?

b) Find the uncertainty in the momentum of the particle.

Assignment #5 Due Mon, Oct 3

Chapter 6: Question 6, 7, 8, Problems 3*, 15, 18, 21, 34**, 46, 54***, Problems below:

Additional problem:

a) Find the energy and degeneracy of the six lowest-energy states
of a particle with mass m in a 2-dimensional infinite square well with
length = width = L. Write your energies in terms of m and L (or
define a useful constant in terms of m and L, and write your energies
in terms of it).

b) For one of the states of the 5th
energy level (be sure to say which one), graph the wavefunction as a
function of x, and on a separate graph, graph the wavefunction as a
function of y. (Extra credit for a good 3-D graph of wavefunction as a
function of x and y in the same graph.)

*add "for free particle"

**Use TISE with SHO potential energy function: V=(1/2)kx^{2}. Alpha is defined in eqn 6.55a. Write your answer in terms of m and k.

***Do the normalization integral.