An Alternative Derivation of the Fernández-Castro Analytic Approximate Expression for the Eigenvalues of the Bounded Quartic Oscillator

摘要

In this note we show that the standard Rayleigh-Schr?dinger (RS) perturbation method gives the same result as the hypervirial pertubative method (HPM), for an approximate analytic expression for the energy eigenvalues of the bounded quartic oscillator. This connection between the HPM and the RS method went unnoticed for a long time, apparently because it was not obvious that the resulting polygamma sums to be evaluated in the RS method could, in fact, be expressed in closed form.