Exact quantization formula for affine linearly energy-dependent potentials

Abstract

Abstract:We construct an exact quantization formula for Schrödinger equations with potentials thatdepend affine linearly on the energy, that is, they contain a term linear in the energy plus an energy-independent term. If such an energy-dependent potential admits a discrete spectrum and its ground state solution is known, our formula predicts the complete energy spectrum in exact form.PACS (2008)