Problem set #5
1.
a.
A function
degree if
where
of
variables
is called a homogeneous function of
is an arbitrary constant. Prove that such a function satisfies
b.
Determine if the potentials
,
and
are homogeneous functions are
not and if they are, determi
Problem set #4
1.
Consider three spin-1/2 particles with spins
Define
and
,
,
and
.
as the total spin. Find a set of eigenvectors for
in terms of the direct products of the spin eigenstates,
, of the individual particles.
2.
Consider a system composed of
Problem set #3
1.
Consider a spin-1/2 particle. Call its spin
and its state vector
where , ,
. Let
and
, its orbital angular momentum
be two functions defined by
are the spherical polar coordinates of the particle,
given function of , and
is a
is a spheri
Problem set #2
1.
Show explicitly that
ion.
commutes with the Hamiltonian for the H
molecule
2.
In the H molecule ion, let be the distance between the protons. Note that
the LCAO approximation developed in class is correct when is large and the
electron i
Problem set #1
1. Consider an electron fixed in space interacting with a constant magnetic field B. Such
a spatially fixed electron can exist in one of two spin states referred to as spin-up and
spin-down. Since this constitutes two possibilities, the dim
The Photoelectric Effect
If light shines on certain metals, electrons are emitted. This is the photoelectric effect.
If the metal is in air, the electrons bounce off air molecules and are almost certainly
rapidly reabsorbed, but if the metal surface is in
Black Body Radiation
But there was one problem that was hard to get a grip on, an apparently blatant
violation of the equipartition of energy. Consider an oven with a small hole in the
door, through which the radiation inside is observed. This oven can be
late its moment of inertia. You can also
measure the combined moment of the wheel
and the mass loads and then calculate the
moment of inertia of the loads alone as the
difference between these two measurements.
This experiment also includes an introductio
Problem set #7
1.
The time-dependent Schrdinger equation for a particle moving in a
potential
subject to an electromagnetic field is
Show that the Schrdinger equation is invariant under a gauge transformation
2.
Suppose a harmonic oscillator with frequenc
Problem Set #6
1.Consider an atom or molecule that has 2 electrons. Let
be the wave
electronic wave function. Suppose the spatial and spin components of
separate such that
where
a.
and
are the eigenvalues of
for each electron.
Suppose the electrons are in