Solution of the Schrödinger equation for a particle in an equilateral triangle

The complete solution for the quantum‐mechanical problem of a particle in an equilateral triangle is derived. By use of projection operators, eigenfunctions belonging explicitly to each of the irreducible representations of the symmetry group C3V are constructed. The most natural definition of the quantum numbers p and q includes not only integers but also nonintegers of the class (1)/(3) and (2)/(3) modulo 1. Some relevant features relating to symmetry and degeneracy are also discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70076/2/JMAPAQ-26-11-2784-1.pd