Tight upper and lower bounds to the eigenvalues and critical parameters of a double well

TL;DR

This paper introduces a rational approximation method to accurately bound eigenvalues and critical parameters of a quartic double-well potential, enhancing precision in quantum mechanical spectral analysis.

Contribution

It presents a novel rational approximation technique that provides tight bounds on eigenvalues and critical parameters for the double-well potential.

Findings

Achieved tight bounds on eigenvalues.

Provided accurate estimates of critical parameters.

Demonstrated effectiveness of the approximation method.

Abstract

By means of a suitable rational approximation to the logarithmic derivative of the wavefunction we obtain tight upper and lower bounds to the eigenvalues and critical parameters of the quartic double-well potential.