Exactly Solvable Asymmetric Double-Well Potentials

Abstract

A model is presented, where an asymmetric double-well potential (DWP) is constructed from several smoothly joined Morse-type components. A complete analytic solution procedure of the quantum-mechanical eigenvalue problem for such DWP model is presented and illustrated. A direct comparison between the quantum-mechanical description and an extended Bohr–Sommerfeld approach is performed. Independent of the DWP analysis, an exact formula for the wavefunction's phase shift is derived