Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

On the Variational Treatment of a Class of Double-Well Oscillators

Version 1 : Received: 4 September 2023 / Approved: 5 September 2023 / Online: 6 September 2023 (02:37:18 CEST)

How to cite: Fernandez, F.; Garcia, J. On the Variational Treatment of a Class of Double-Well Oscillators. Preprints 2023, 2023090309. https://doi.org/10.20944/preprints202309.0309.v1 Fernandez, F.; Garcia, J. On the Variational Treatment of a Class of Double-Well Oscillators. Preprints 2023, 2023090309. https://doi.org/10.20944/preprints202309.0309.v1

Abstract

We compare the well known Rayleigh-Ritz variational method (RRVM) with a recently proposed approach based on supersymmetric quantum mechanics and the Gram-Schmidt orthogonalization method (SSQMGS). We apply both procedures to a particular class of double-well harmonic oscillators that had been conveniently chosen for the application of the latter approach. The RRVM eigenvalues converge smoothly from above providing much more accurate results with less computational effort. Present results show that the unproved SSQMGS upper bounds do not hold.

Keywords

Double-well oscillator; upper bounds; Rayleiigh-Ritz; Gram-Schmidt

Subject

Physical Sciences, Mathematical Physics

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