Energy levels of a particle in an infinite potential well with identical square-potential barriers

Abstract

We have evaluated the energy levels of a particle in an infinite potential well containing identical square-potential barriers of equal width and separation, in a symmetric as well as an asymmetric arrangement, as functions of the number and height of the potential barriers. For this purpose we have derived analytical equations for the energy eigenvalues which can be solved with a personal computer. We show plots of the normalized energy levels of particles in potential wells containing up to three identical square-potential barriers with heights varying from zero to infinity. These can be applied to models of inversion and libration of molecules, electronic states in dye molecules, quantum well structures, etc.