On the variational treatment of a class of double-well oscillators

• URL: http://arxiv.org/abs/2312.00004v1
• Date: Thu, 17 Aug 2023 14:59:04 GMT
• Title: On the variational treatment of a class of double-well oscillators
• Authors: Francisco M. Fern\'andez and Javier Garcia
• Abstract summary: We compare the well known Rayleigh-Ritz variational method (RRVM) with a recently proposed approach based on supersymmetric quantum mechanics. We show that the unproved SSQMGS upper bounds do not hold.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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