Analytic expression for exact-ground-state energy based on an operator method for a class of anharmonic potentials

Abstract

The full spectrum of a physical system is extracted with arbitrarily potentials using the shift operator method. The method is applied to a one-dimensional oscillator with anharmonic potentials. The supersymmetric quantum mechanics (SQM) is analyzed as a special case of a nonlinear algebraic operator method. Analytical results checked the accuracy of the state-dependent diagonalization.