What makes matrix mechanics matrix mechanics?

[ardie]

ok there's one detail that I have ignored that may have been what you were looking for. wave mechanics failed to comply with the relativistic energy. at the time dirac solved this by introducing matrices that solved the wave equation if inserted, instead of just the single wave function. for details I recommend:http://en.wikipedia.org/wiki/Dirac_equation
the idea is that in the new tonsorial equation, the wave function must be a tensor itself, thereby introducing matrix mechanics to wave physics.

 

[Einstein Mcfly]

ok there's one detail that I have ignored that may have been what you were looking for. wave mechanics failed to comply with the relativistic energy. at the time dirac solved this by introducing matrices that solved the wave equation if inserted, instead of just the single wave function. for details I recommend:http://en.wikipedia.org/wiki/Dirac_equation
the idea is that in the new tonsorial equation, the wave function must be a tensor itself, thereby introducing matrix mechanics to wave physics.

No, this is not my question. My question is in starting from first principals looking to calculate the total energy of an atom or molecule, how would I accomplish this using "matrix mechanics" and how would I accomplish this using "wave mechanics". I know I must get the same answer regardless but they are distinct techniques. I know how I DO do this in calculations, but I don't know to which method what I do belongs or if it's some mixture of both.