Particle in a spherical potential well of energy dependent depth

Abstract

The Schrödinger equation is solved for a spherical finite well potential whose depth depends linearly on the energy. The energy spectrum is derived as a function of the well’s dimensional parameter and the slope of the energy dependence. The latter is found to have a finite domain of values which assures the existence of bound states. The evolution of the energy spectrum and the corresponding wave functions as a function of the slope parameter is exemplified within a numerical analysis. The upper limit of the slope parameter offers an infinite spectrum which is compared to the case of the infinite spherical well case. A physical application of this limiting case is presented for the shape fluctuation phenomena in atomic nuclei.