Article
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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
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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