dorsal/arxiv
View SchemaSupersymmetry and the Hartmann Potential of Theoretical Chemistry
| Authors | Gardo Garnet Blado |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9602005 |
| URL | https://arxiv.org/abs/quant-ph/9602005 |
| Journal | Theoretica Chimica Acta, volume 94, July, 1996, page 53 |
Abstract
The ring-shaped Hartmann potential $ V = \eta \sigma^{2} \epsilon_{0} \left( \frac{2 a_{0}}{r} - \frac{\eta a_{0}^{2}}{r^{2} sin^{2} \theta} \right) $ was introduced in quantum chemistry to describe ring-shaped molecules like benzene. In this article, the supersymmetric features of the Hartmann potential are discussed. We first review the results of a previous paper in which we rederived the eigenvalues and radial eigenfunctions of the Hartmann potential using a formulation of one-dimensional supersymmetric quantum mechanics (SUSYQM) on the half-line $\left[ 0, \infty \right)$. A reformulation of SUSYQM in the full line $\left( -\infty, \infty \right)$ is subsequently developed. It is found that the second formulation makes a connection between states having the same quantum number $L$ but different values of $\eta \sigma^{2}$ and quantum number $N$. This is in contrast to the first formulation, which relates states with identical values of the quantum number $N$ and $\eta \sigma^{2}$ but different values of the quantum number $L$.
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"abstract": "The ring-shaped Hartmann potential $ V = \\eta \\sigma^{2} \\epsilon_{0} \\left(\n\\frac{2 a_{0}}{r} - \\frac{\\eta a_{0}^{2}}{r^{2} sin^{2} \\theta} \\right) $ was\nintroduced in quantum chemistry to describe ring-shaped molecules like benzene.\nIn this article, the supersymmetric features of the Hartmann potential are\ndiscussed. We first review the results of a previous paper in which we\nrederived the eigenvalues and radial eigenfunctions of the Hartmann potential\nusing a formulation of one-dimensional supersymmetric quantum mechanics\n(SUSYQM) on the half-line $\\left[ 0, \\infty \\right)$. A reformulation of SUSYQM\nin the full line $\\left( -\\infty, \\infty \\right)$ is subsequently developed. It\nis found that the second formulation makes a connection between states having\nthe same quantum number $L$ but different values of $\\eta \\sigma^{2}$ and\nquantum number $N$. This is in contrast to the first formulation, which relates\nstates with identical values of the quantum number $N$ and $\\eta \\sigma^{2}$\nbut different values of the quantum number $L$.",
"arxiv_id": "quant-ph/9602005",
"authors": [
"Gardo Garnet Blado"
],
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],
"journal_ref": "Theoretica Chimica Acta, volume 94, July, 1996, page 53",
"title": "Supersymmetry and the Hartmann Potential of Theoretical Chemistry",
"url": "https://arxiv.org/abs/quant-ph/9602005"
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