The beauty of Heisenberg's matrix mechanics

This is a contributed talk to the 2024 March meeting of the American Physical Society that discusses the details of how one can use Heisenberg's matrix mechanics to derive the canonical commutation relation between position and momentum and also shows how one solves for the energy eigenvalues of the simple harmonic oscillator in quantum mechanics.

[@lepidoptera9337]

I agree. We should be teaching this (and Dirac's "derivation" of the Dirac equation) in undergrad physics to motivate what creative thinking in physics looks like.

[@davidrandell2224]

QM classicalized in 2010. Forgotten Physics website uncovers the hidden variables and constants and the bad math of Wien, Schrodinger, Heisenberg, Einstein, Debroglie,Planck, Bohr etc.

[@wp4297]

incredibily good and short review of the basics and origin of matrix mechanics. Precious stuff. Thanks a lot

[@quantum4everyone]

You are very welcome.

[@5ty717]

Succinct and wondrous. Beautiful. thx for posting.

[@quantum4everyone]

Glad you liked it

[@5ty717]

Beautiful…

[@Andres-is3lj]

Could you use the matrix mechanics to solve the rigid rotor? Thanks professor

[@quantum4everyone]

Yes you can, and the derivation is essentially done in many textbooks. Heisenberg, however, did it wrong in his first paper. Because these matrices are finite dimensional for a specific angular momentum representation, they are easier to work with.