I need to find the wavefunctions of the stationary states of a 3d square potential well with its boundaries defined by a triangular prism - like the one illustrated on the wikipedia page: https://en.wikipedia.org/wiki/Triangular_prism
The potential well (viewed in 1-d cross section) is a simple square potential well, and can be either finite (0 outside, -V inside) or infinite (0 inside, ∞ outside), both would be reasonable approximations for my purposes.
I.e. the potential is something like this in cross-section, but its full 3-D shape is that of the triangular prism:
[Any solution for a close approximation of this geometry may also be helpful (for example, if the problem is easier to solve for a prism with a Reuleaux triangular cross-section instead of equilateral, or for a potential well described by a continuous function or something, it may be close enough).]
Because of the reduced symmetry compared to the textbook cylindrical or spherical cases, I am not sure how to approach this.
Is anyone able to point me in the direction of a solution? Many thanks!