Physics blogs

Let us start building a list of interesting blogs in Physics and in general in science.
These blogs are being kept by some of the most creative minds in Physics and we
hope to benefit from them. First of them, listed a day ago (on the right margin) is
The Reference Frame by Czech physicist Lubos Motl who has made significant
contributions to theoretical high energy physics and string theory. We may or may not subscribe (I don't, for one) to
his views on various issues (particularly political). But being from Kerala, where
the weight of a scientific theory is judged by the length of the beard of the proponent,
I strongly recommend this blog. Not the least because the author does not sport a
beard, rather because he does not mind taking the so called "high and mighty"
to task for their flawed stance on various issues, physics or non-physics.
In addition, the above blog also provides link to many physics web resources/blogs
of import.

Do take a look at the list once a while !

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).

Potential well - transition processes

This note is an update of the previous one with a new section added. Parts of
the section has been modified. The newly added section deals with only transition
processes - reflection and transmission. As explained in the class, it is somewhat
too simple to study these for the case of a finite potential well that extends to
infinity on both sides. It is instructive to do this for the case of a potential barrier
to see a worthy application with use in real physical systems - alpha decay being
a fine example. See problem #4 in the Problem set 02 (click). This note should
help you do it. As mentioned previously, the note contains what was discussed in
the class on potential well but written in a way to a more satisfactory way. Most
textbooks do not care to give clear derivations as it is a bit hazy to do it in position
space representations, namely, in terms of wavefunctions. Here we make it clearer
using bra-ket notations and provide a convincing derivation of the reflection
coefficient.


Modified note on Potential well (Click here to download)

Energy spectrum - finite potential well

Sorry ! That was too long a 24 hours.

The lecture note has been prepared in a different order from what has been done below.
It contains slightly different and better treatment of the one dimensional finite potential
well than in the class. The note has been split up into two parts. Part I discussion
of energy eigenvalues and eigenfunctions. The allowed energy spectrum has been explained comprehensively. We will make use of this information in part II to study the transition processes like reflection/transmission.

Here is Part I (click here to download)


Feel free to post comments/questions.

Happy times !

The beginning...

PhyCUKians will discuss mostly physics and some non-physics stuff here in these blogs. Await an update in another 24 hours.