Monday, November 19, 2012

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The coolest thing in the book so far is a historical reference to Heisenberg.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.











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