Tight upper and lower bounds for energy eigenvalues of the Schrödinger equation

Abstract

A method is presented for the calculation of tight upper and lower bounds for the energy eigenvalues of the Schr\"odinger equation. The method is based on a rational functional approximation for the series expansion of the solution of the Riccati equation for the logarithmic derivative of the wave function. Specific applications for one-dimensional anharmonic oscillators and for the Yukawa potential are given, and the present results are compared with those obtainable by other procedures.