On the doubly anharmonic oscillator in an elastic environment in the presence of a point-like defect

Abstract

Abstract We have investigated a doubly anharmonic oscillator in an elastic medium characterized by the presence of a point-like defect, where we obtain analytically your solution of bound states. We show that it is not possible to obtain a unique expression for the energy profile of the quantum system, but rather an expression corresponding to each radial mode of the system. Furthermore, an interesting quantum effect is presented: the three parameters that characterize the doubly anharmonic oscillator are quantized, that is, they depend on the quantum numbers of the system.