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."
Yea sounds like it, I took the standard math track at my college and never had any problem with my upper level physics courses but most of my fellow students constantly complained their lack of math understanding was severely hurting their physics education.
I wonder if most physics curriculum's underestimate the amount of time it takes to truly become competent with calculus/DE tools. I may of only escaped because I loved math and did a lot of self study out of pleasure.
I think they are well aware of how few hours they have to teach physics. The debate is more, which classes can be dropped and replaced with a math course, in order that the students can have a deeper understanding of the underlying math?
More specifically, which of thermodynamics, optics, particle/nuclear physics, solid state, lab courses, E&M, classical mechanics, or quantum mechanics do you think should be dropped from the physics requirement, and which math course should replace it?
Or should the liberal arts requirements be reduced? Or should physics become a 5 year program?
