I'm not entirely sure how knowing a standard undergrad PDE course would help in understanding the various physicist-specific techniques that go into solving the Schroedinger equation. I don't really understand why OP thought they needed to grok ODEs before being able to solve PDEs; the two fields have relatively small intersection.
Physics has more than just the Schrödinger equation. My undergrad PDE course helped immensely in my graduate level physics qualifying example. One question was on the heat equation and the other an E&M problem, both in a rectilinear coordinate system.
With a solid foundation in second-order PDEs, it's a matter of setting up the boundary conditions and solving for the Fourier series. The boundary conditions were superimposeable combinations of simpler forms, so it was mostly a matter of determining the correct Fourier series for those forms, then simplifying.
The OP probably didn't understand the distinction between ODEs and PDEs because of a lack of experience.
> Physics has more than just the Schrödinger equation.
It was a course in Quantum Mechanics, specifically.
> With a solid foundation in second-order PDEs, it's a matter of setting up the boundary conditions and solving for the Fourier series. The boundary conditions were superimposeable combinations of simpler forms, so it was mostly a matter of determining the correct Fourier series for those forms, then simplifying.
In a usual undergrad course on QM, e.g., following Griffiths, one only solves SE with particular choices of potential -- usually only infinite well and QHO, and maybe a double well to illustrate tunneling. Neither really requires a background in Fourier series.
Ahh, I see. I left the train of discussion, and reinterpreted "physics" in the broad sense, rather than actual topic of "physics for an undergraduate quantum course."
