dorsal/arxiv
View SchemaBound States and Band Structure - a Unified Treatment through the Quantum Hamilton - Jacobi Approach
| Authors | S. Sree Ranjani, A. K. Kapoor, P. K. Panigrahi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0506204 |
| URL | https://arxiv.org/abs/quant-ph/0506204 |
| DOI | 10.1016/j.aop.2005.05.004 |
| Journal | Ann of phys, Vol 320, Issue 1, 164 (2005) |
Abstract
We analyze the Scarf potential, which exhibits both discrete energy bound states and energy bands, through the quantum Hamilton-Jacobi approach. The singularity structure and the boundary conditions in the above approach, naturally isolate the bound and periodic states, once the problem is mapped to the zero energy sector of another quasi-exactly solvable quantum problem. The energy eigenvalues are obtained without having to solve for the corresponding eigenfunctions explicitly. We also demonstrate how to find the eigenfunctions through this method.
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"abstract": "We analyze the Scarf potential, which exhibits both discrete energy bound\nstates and energy bands, through the quantum Hamilton-Jacobi approach. The\nsingularity structure and the boundary conditions in the above approach,\nnaturally isolate the bound and periodic states, once the problem is mapped to\nthe zero energy sector of another quasi-exactly solvable quantum problem. The\nenergy eigenvalues are obtained without having to solve for the corresponding\neigenfunctions explicitly. We also demonstrate how to find the eigenfunctions\nthrough this method.",
"arxiv_id": "quant-ph/0506204",
"authors": [
"S. Sree Ranjani",
"A. K. Kapoor",
"P. K. Panigrahi"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/j.aop.2005.05.004",
"journal_ref": "Ann of phys, Vol 320, Issue 1, 164 (2005)",
"title": "Bound States and Band Structure - a Unified Treatment through the Quantum Hamilton - Jacobi Approach",
"url": "https://arxiv.org/abs/quant-ph/0506204"
},
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