- #1
quantumlaser
- 16
- 0
I'm a bit embarrased to ask this (thats why I'm asking here and not asking one of my professors), as a grad student in Physics I've had a good deal of quantum mechanics, but one thing I haven't fully understood yet is the mechanism in the Schrodinger Equation that forces eigenvalue quantization (energy, angular momentum, etc...) in bound state solutions. For quantum well potentials, energy quantization is forced by the boundary conditions, but in the harmonic oscillator and hydrogen atom potentials, the eigenvalue quantization seems to just pop out as a consequence of the math. It seems there should be some deeper explanation as to why the bound state eigenvalues are quantized. Could someone enlighten me on this?