Matrix Mechanics

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1. Nov 7, 2014

Pollock

I would like to know more about how Heisenberg developed his matrix mechanics.He wanted to represent the quantum state in terms of observable quantities such as spectral frequencies and intensities,rather than via the more abstract wave function of Schrodinger.But how did he assemble the arrays of numbers that Born eventually recognised as non-commuting matrices ?.Can someone tell me or refer me to an easily understandable review or paper ?.I guess I would find Heisenbergs original papers too difficult.

2. Nov 7, 2014

Simon Bridge

... in that case, nobody can tell you and is unlikely to be able to get you a review with more details than you can find from googling for history books. I doubt anyone actually knows anyway.
The process someone went through, of getting to a new model, representation, or paradigm is usually not very useful to others - creativity is so personal.
However, someone will be able to get you some idea if you would tell us what you hope to gain from the answer.

3. Nov 7, 2014

Dr Transport

Last edited by a moderator: May 7, 2017
4. Nov 7, 2014

bhobba

The following may help:
http://www.mathpages.com/home/kmath698/kmath698.htm

Actually Schroedinger developed wave mechanics after matrix mechanics and it was a competitor for a while. The reason Schroedinger hypothesised his equation is also quite interesting:
http://arxiv.org/abs/1204.0653

Even more interesting was how Dirac dramatically extended Heisenbergs ideas by means of analogies to Poisson brackets and his so called q numbers:
http://arxiv.org/pdf/1006.4610.pdf

Eventually Dirac, in late 1926, came up with his transformation theory, which is basically QM as we know it today, that showed all three approaches were really the same. This also has an interesting history, being tied up with that damnable Dirac delta function so loved by applied mathematicians, but sending pure mathematicians insane: