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)

Some fun

Here is a fun problem which you may want to look at.



Four rockets are placed at the corners of a square of side 20 km. Each of the
rockets moves in such a way that it remains pointed towards the nose of the one
next to it in clockwise sense. Let us say the rockets move at a speed of 4 km per
sec each. Find out whether they will collide, if yes the time and location of collision
and their trajectory. (Source : Puzzle Math, George Gamow)

There is a quick way to guess the answer, but find the answer using our old
classical mechanics.

Problem set 03

Problem set 03 stresses largely on bread and butter operator algebra, foundational
principles of quantum mechanics and one dimensional problems, especially, the
harmonic oscillator. I noticed some typos in the hard copy circulated in the class.
I will make the corrections in the next class. Nevertheless, here is the corrected
version of problem set 03 (click & download).