The QES sextic and Morse potentials: exact WKB condition and supersymmetry
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909327601696768 |
|---|---|
| author | Contreras-Astorga, Alonso Escobar-Ruiz, A. M. |
| author_facet | Contreras-Astorga, Alonso Escobar-Ruiz, A. M. |
| contents | In this paper, as a continuation of [Contreras-Astorga A., Escobar-Ruiz A. M. and Linares R., \textit{Phys. Scr.} {\bf99} 025223 (2024)] the one-dimensional quasi-exactly solvable (QES) sextic potential $V^{\rm(qes)}(x) = \frac{1}{2}(ν\, x^{6} + 2\, ν\, μ\,x^{4} + \left[μ^2-(4N+3)ν\right]\, x^{2})$ is considered. In the cases $N=0,\frac{1}{4},\,\frac{1}{2},\,\frac{7}{10}$ the WKB correction $γ=γ(N,n)$ is calculated for the first lowest 50 states $n\in [0,\,50]$ 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 $\mathfrak{sl}_2(\mathbb{R})$ Lie algebra and vanishing WKB correction $γ=0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_18311 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The QES sextic and Morse potentials: exact WKB condition and supersymmetry Contreras-Astorga, Alonso Escobar-Ruiz, A. M. Quantum Physics Mathematical Physics In this paper, as a continuation of [Contreras-Astorga A., Escobar-Ruiz A. M. and Linares R., \textit{Phys. Scr.} {\bf99} 025223 (2024)] the one-dimensional quasi-exactly solvable (QES) sextic potential $V^{\rm(qes)}(x) = \frac{1}{2}(ν\, x^{6} + 2\, ν\, μ\,x^{4} + \left[μ^2-(4N+3)ν\right]\, x^{2})$ is considered. In the cases $N=0,\frac{1}{4},\,\frac{1}{2},\,\frac{7}{10}$ the WKB correction $γ=γ(N,n)$ is calculated for the first lowest 50 states $n\in [0,\,50]$ 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 $\mathfrak{sl}_2(\mathbb{R})$ Lie algebra and vanishing WKB correction $γ=0$. |
| title | The QES sextic and Morse potentials: exact WKB condition and supersymmetry |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2409.18311 |