Monday, March 25, 2013

The Week in Preview, March 25th 2013

A quick review of what I'll be looking at over the course of the upcoming week.  This is as much to get my own thoughts in order as anything else.


Quantum Mechanics:
I'll be working on still more uncertainty and harmonic oscillator problems in QM this week.  What a surprise right :)  Specifically, this week, I'll be calculating matrix elements for both position and momentum squared using both the Hermite polynomial recursion operators and the ladder operators.  These are covered in chapters 5 and 10 in Merzbacher.  I was playing around with one of the recursion relations (picture 1)



 for Hermitian polynomials earlier in the year and wound up with the following kind of interesting table.  You can see the n level of the wave function moved out of the way by the successive application of the recursion formula which amounts to the successive application of the x operator, or a sum of the raising and lowering operators (picture 2).


I know a lot of students, (including me), that think Jackson's EM book is merely a very thinly veiled math methods book.  While looking through old American Journal of Physics back issues, I found a review for another book by Jackson was apparently more appropriately titled than his 'EM' book.  This one is about the math required for quantum mechanics, "Mathematics for Quantum Mechanics: An Introductory Survey of Operators, Eigenvalues, and Linear Vector Spaces (Dover Books on Mathematics)".  At only $6.50 on Amazon, at least the price is right, but as usual, I'll be using the library's copy for free.

Hirsch Based Superconductor Research:
There are a few things I have to look into regarding the upcoming experimental research I'm doing.  In the 1930's it was documented that lead, (Pb), had an intermediate state between its superconducting and normal states[1][2].  This is important information to have since what we'd ideally like to do is 'instantly' quench the Pb superconducting sample using a magnetic field.

The design of the superconducting magnet that will provide the quenching field will also get done this week, so look for a few graphs and calculations.  I got to take a look at the 1/18000 of an inch diameter superconducting wire that can carry 55 amps last week.  It was cool!

Casimir Research:
I have a presentation due on this on Friday at our local student research week exposition.  In addition to that, I'm working on calculating various aspects of the asymptotic Bessel function approximation for the fields contained in the annular wedge problem we're working on.

And now, off to work.


References:
1.  Intermediate state in lead superconductors
http://dx.doi.org/10.1098%2Frspa.1936.0129
Shoenberg D. (1936). The Magnetization Curves of a Supraconducting Sphere and Ring, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 155 (886) 712-726. DOI:

2.  More on the intermediate state using alternating current magnetic fields
http://dx.doi.org/10.1017%2FS0305004100077690
Shoenberg D. (1937). Superconductors in Alternating Magnetic Fields, Mathematical Proceedings of the Cambridge Philosophical Society, 33 (04) 559. DOI:

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