dorsal/arxiv
View SchemaOn Exactness Of The Supersymmetric WKB Approximation Scheme
| Authors | R. S. Bhalla, A. K. Kapoor, P. K. Panigrahi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9512019 |
| URL | https://arxiv.org/abs/quant-ph/9512019 |
| DOI | 10.1103/PhysRevA.54.951 |
Abstract
Exactness of the lowest order supersymmetric WKB (SWKB) quantization condition $\int^{x_2}_{x_1} \sqrt{E-\omega^2(x)} dx = n \hbar \pi$, for certain potentials, is examined, using complex integration technique. Comparison of the above scheme with a similar, but {\it exact} quantization condition, $\oint_c p(x,E) dx = 2\pi n \hbar$, originating from the quantum Hamilton-Jacobi formalism reveals that, the locations and the residues of the poles that contribute to these integrals match identically, for both of these cases. As these poles completely determine the eigenvalues in these two cases, the exactness of the SWKB for these potentials is accounted for. Three non-exact cases are also analysed; the origin of this non-exactness is shown to be due the presence of additional singularities in $\sqrt{E-\omega^2(x)}$, like branch cuts in the $x-$plane.
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"abstract": "Exactness of the lowest order supersymmetric WKB (SWKB) quantization\ncondition $\\int^{x_2}_{x_1} \\sqrt{E-\\omega^2(x)} dx = n \\hbar \\pi$, for certain\npotentials, is examined, using complex integration technique. Comparison of the\nabove scheme with a similar, but {\\it exact} quantization condition, $\\oint_c\np(x,E) dx = 2\\pi n \\hbar$, originating from the quantum Hamilton-Jacobi\nformalism reveals that, the locations and the residues of the poles that\ncontribute to these integrals match identically, for both of these cases. As\nthese poles completely determine the eigenvalues in these two cases, the\nexactness of the SWKB for these potentials is accounted for. Three non-exact\ncases are also analysed; the origin of this non-exactness is shown to be due\nthe presence of additional singularities in $\\sqrt{E-\\omega^2(x)}$, like branch\ncuts in the $x-$plane.",
"arxiv_id": "quant-ph/9512019",
"authors": [
"R. S. Bhalla",
"A. K. Kapoor",
"P. K. Panigrahi"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.54.951",
"title": "On Exactness Of The Supersymmetric WKB Approximation Scheme",
"url": "https://arxiv.org/abs/quant-ph/9512019"
},
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