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

Schr\"{o}dinger's equation is used for a quantum particle confined to move in a circle of radius R. the particle encounters a zero potential almost everywhere, except for when it comes across delta function potentials of strength p, situated symmetrically around the ring. The energy spectrum for this system is analyzed in various cases of attractive or repulsive potentials and positive or negative total energy of the particle.