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: 10.1098/rspa.1936.0129

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: 10.1017/S0305004100077690

More Cowbell! Record Production using Google Forms and Charts

First, the what : This article shows how to embed a new Google Form into any web page. To demonstrate ths, a chart and form that allow blog readers to control the recording levels of each instrument in Blue Oyster Cult's "(Don't Fear) The Reaper" is used. HTML code from the Google version of the form included on this page is shown and the parts that need to be modified are highlighted. Next, the why : Google recently released an e-mail form feature that allows users of Google Documents to create an e-mail a form that automatically places each user's input into an associated spreadsheet. As it turns out, with a little bit of work, the forms that are created by Google Docs can be embedded into any web page. Now, The Goods: Click on the instrument you want turned up, click the submit button and then refresh the page. Through the magic of Google Forms as soon as you click on submit and refresh this web page, the data chart will update immediately. Turn up the:

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There's an assymetry to the form of the two Maxwell's equations shown in picture 1. While the divergence of the electric field is proportional to the electric charge density at a given point, the divergence of the magnetic field is equal to zero. This is typically explained in the following way. While we know that electrons, the fundamental electric charge carriers exist, evidence seems to indicate that magnetic monopoles, the particles that would carry magnetic 'charge', either don't exist, or, the energies required to create them are so high that they are exceedingly rare. That doesn't stop us from looking for them though! Keeping with the theme of Fairbank[1] and his academic progeny over the semester break, today's post is about the discovery of a magnetic monopole candidate event by one of the Fairbank's graduate students, Blas Cabrera[2]. Cabrera was utilizing a loop type of magnetic monopole detector. Its operation is in concept very sim

Copasetic Flow

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