Hello all. I haven't worked hard enough yet (reading the original papers etc) to really get at the differences here, but I thought I'd ask the local experts if there was more to it than I already know. From what I've gathered so far, Heisenberg's formulation dealt only with matrix representations of operators expressed in some basis and derived observables from them (I assume by diagonalizing them). There were no "orbitals" in the sense of functions defined in space with particular "shapes", because all he cared about was finding a way to get the spectra correct. If I'm not right up to this point, please correct me.... So, now when I'm, say, doing quantum chemistry and I have the fock operator or some such thing and I'm diagonalizing it to get orbitals and energies and doing the rinse and repeat needed to converge, and I doing "matrix mechanics"? Is phrasing the problem in terms of matricies rather than a differential equation all it takes, or am I just using the algebra of matricies to do Schrodinger wave mechanics? I know that they're necessarily equivalent, but its the differences in perspective that I'm interested in. Thanks for any helpful comments.