Circular arrangements of atoms: solving Schr\"{o}dinger's equation for the energy spectrum

Placing atoms in a circular arrangement enables us to use Schr\"{o}dinger's time-independent equation in combination with specific boundary conditions in order to solve for the system's energy spectrum. In addition, symmetry constraints facilitate the investigation of various configurations of atoms, including the situation in which atoms are of different species. We use MAPLE to represent graphically the solutions of the resulting transcendent equations.