HIGHLY ACCURATE CALCULATION OF THE REAL AND COMPLEX EIGENVALUES OF ONE-DIMENSIONAL ANHARMONIC OSCILLATORS

Abstract

We draw attention on the fact that the Riccati-Padé method developed some time ago enables the accurate calculation of bound-state eigenvalues as well as of resonances embedded either in the continuum or in the discrete spectrum. We apply the approach to several one-dimensional models that exhibit different kind of spectra. In particular we test a WKB formula for the imaginary part of the resonance in the discrete spectrum of a three-well potential.

Keywords

• anharmonic oscillators, bound states, resonances, Riccati-Padé method, WKB asymptotic expression