Partly motivated as a follow-up to the Oppenheimer biography I recently read, and partly to get a clearer idea of Quantum Mechanics than I had (for my course on Spectral Theory in Hilbert Spaces, which just ended; though the posted lecture notes are a bit lagging, I will post a complete version soon…), I have just finished reading *“The conceptual development of quantum mechanics*“, by M. Jammer (a book which seems unfortunately to have almost no online presence; I got the reference from another book and borrowed it from the ETH library).

This was extremely interesting; the author assumed rather more knowledge of classical physics than I could claim to remember from my studies, but since I had been reading other accounts of (modern) Quantum Mechanics for mathematicians, I was not entirely lost, and I was quite fascinated. I won’t say anything about the physical aspects, but one quite amazing thing that emerges is how quickly the formalism emerged from 1925 to 1929. Not only did matrix mechanics (Heisenberg, 1925), Dirac’s formalism 1925–26), Schrödinger’s wave mechanics (1926) all come out in barely more than a year, but also Nordheim, Hilbert and von Neumann had the time to do a first mathematical reformulation in 1927 before von Neumann gave the formalization in terms of the spectral theorem for unbounded self-adjoint operators in 1929. (I note in passing that von Neumann was quite footnote-happy, at least in that paper).

Another thing I didn’t know is that the Diract δ function was first discussed by Kirchhoff in 1882 (in a paper on optics), who already explained its origin as a limit of Gaussians with variance going to 0.

Interesting post.

About the Dirac distribution, I have heard that Joseph Fourier gave a first definition of it too in his work on the Heat equation. If I remember correctly, it was described as the limit of a sinc(alpha t)/alpha when alpha tends to 0.

Yes the years 1929-1925 were truly anni mirabili.

About quantum mechanics vs.mathematics:

A well-known difficulty in a first introduction to multilinear algebra is that a generic element of the tensor product of two vector spaces is not the product of two vectors from these spaces (but a sum of such products).

It is really amazing that this most shocking aspect of quantum mechanics-the entanglement of two quantum systems (Einstein’s “spukhafte Fernwirkungen”)-has as exact mathematical translation this feature of tensor algebra.

Is this taught at ETH or are professors there afraid of Einstein’s spook?

A research group on that:

http://quantum-history.mpiwg-berlin.mpg.de/main/index.html