Physics 224   Fall 2001

		Discoveries and Inventions of Modern Physics 		due 11:00 am Tuesday Oct. 2

PROBLEM SET 1

1.

Eisberg and Resnick: Problem 6.19 (Note the difference between ``Questions'' and ``Problems'' in Eisberg and Resnick.)

2.

Eisberg and Resnick: Problem 6.20

3.

In class we counted the states in a 3D box. Do the same for a 2D box with periodic boundary conditions. In particular find

(a)

the energy eigenstates E(n_x,n_y)

(b)

the density of states $N(\omega)$ for photons that have only one polarization

4.

Consider a nonrelativistic free particle in a cubic container of edge length L and volume V=L³. Assume that the particle is confined in the container so that the potential is zero inside the container and infinite outside.

(a)

Each quantum state s of this particle has a corresponding kinetic energy $\varepsilon_{s}$ which depends on V. What is $\varepsilon_{s}(V)$?

(b)

Find the contribution to the gas pressure $p_{s}=-(\partial \varepsilon_{s}/\partial V)$ of a particle in this state in terms of $\varepsilon_{s}$ and V.

(c)

Use this result to show that the mean pressure <p> of any ideal gas of particles is always related to its mean total kinetic energy <E>by $<p>=\frac{2}{3}<E>/V$.

5.

Consider the case of the orbital angular momentum quantum number $\ell=2$ and the spin angular momentum number s=1/2.

(a)

What are the possible values of the total angular momentum number j? ( $\vec{J}=\vec{L}+\vec{s}$)

(b)

For each value of j, what are the possible values of j_z?