2024/09/26 by Alonso Contreras-Astorga, Contreras-Astorga, Alonso, A. M. Escobar-Ruiz +1 · 2 citations
Earth and Planetary Sciences · Materials Science · Physics and Astronomy · #FOS: Physical sciences #High-pressure geophysics and materials #Mathematical Physics (math-ph) #Organic and Molecular Conductors Research #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2409.18311
openalex publication_date 2024/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, as a continuation of [Contreras-Astorga A., Escobar-Ruiz A. M. and Linares R., Phys. Scr. \bf99 025223 (2024)] the one-dimensional quasi-exactly solvable (QES) sextic potential V\rm(qes)(x) = (1)/(2)(ν x6 + 2 ν μ x4 + [μ2-(4N+3)ν] x2) is considered. In the cases N=0,(1)/(4), (1)/(2), (7)/(10) the WKB correction γ=γ(N,n) is calculated for the first lowest 50 states n∈ [0, 50] using highly accurate data obtained by the Lagrange Mesh Method. Closed analytical approximations for both γ and the energy E=E(N,n) of the system are constructed. They provide a reasonably relative accuracy |Δ| with upper bound \lesssim 10-3 for all the values of (N,n) studied. Also, it is shown that the QES Morse potential is shape invariant characterized by a hidden \mathfraksl2(ℝ) Lie algebra and vanishing WKB correction γ=0.