Problem Set 04

Problem Set 04 mostly stresses on 3 dimensional exactly solvable problems
discussed in the class. It basically aims to give you a practice on computations
with angular momentum and hydrogen atom eigenfunctions. The physical
significance of these eigenfunctions become clear once you compute the dipole
and quadrupole moments in the last problem. Remember that we really do not
have a charge density, so to say, as we have seen in electrostatics to compute
these moments with. But we have a probability distribution for the charged
particle. So the moments here are not computed weighted with this charge
density. Simply put, here the probability density plays the role of the charge
density.

Laplace-Runge-Lenz vector K is another quantity that is conserved for a central
potential of the form 1/r. This means as usual that as the hydrogen atom evolves
in time, LRL vector remains the same. So K must commute with the Hamiltonian
of the hydrogen atom.

Here is Problem Set 04 (click here to download)