Heisenberg, Dirac, and Matrix Quantum Mechanics

I've been reading an excellent quantum mechanics book by K.T. Hecht this week. The book is very complete, and heavy on worked examples. The level of complexity is much higher than Griffiths, but there are many, many worked examples. You don't run into the key bit of information you need being encrypted into a homework problem. If you've read Griffiths, you know what I mean.

The coolest thing in the book so far is a historical reference to Heisenberg. Hecht points out in less than a page how Heisenberg arrived at the matrix formulation of quantum mechanics. Starting out with the model of the Bohr atom's energy levels, he first noted that the energy was dependent on the frequency of the emitted radiation. This suggested a model similar to a Fourier series. Heisenberg then noted that there were two indices, n and m, and posited that the Fourier model at the atomic scale would utilize a matrix of coefficients as opposed to a list. The rest was just (lots and lots of) details.

If you're near a university that was a subscription to the Proceedings of the Royal Society and you'd like to see those details worked out in English rather than the original German, check out this great article from Dirac. It very clearly spells out what Heisenberg was up to and as a bonus may be the first place the Dirac delta function was introduced.

Comments

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:

Cool Math Tricks: Deriving the Divergence, (Del or Nabla) into New (Cylindrical) Coordinate Systems

Now available as a Kindle ebook for 99 cents ! Get a spiffy ebook, and fund more physics The following is a pretty lengthy procedure, but converting the divergence, (nabla, del) operator between coordinate systems comes up pretty often. While there are tables for converting between common coordinate systems , there seem to be fewer explanations of the procedure for deriving the conversion, so here goes! What do we actually want? To convert the Cartesian nabla to the nabla for another coordinate system, say… cylindrical coordinates. What we’ll need: 1. The Cartesian Nabla: 2. A set of equations relating the Cartesian coordinates to cylindrical coordinates: 3. A set of equations relating the Cartesian basis vectors to the basis vectors of the new coordinate system: How to do it: Use the chain rule for differentiation to convert the derivatives with respect to the Cartesian variables to derivatives with respect to the cylindrical variables. The chain

The Valentine's Day Magnetic Monopole

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

Search This Blog