dorsal/arxiv
View SchemaCalculation of Band Edge Eigenfunctions and Eigenvalues of Periodic Potentials through the Quantum Hamilton - Jacobi Formalism
| Authors | S. Sree Ranjani, A. K. Kapoor, P. K. Panigrahi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0312041 |
| URL | https://arxiv.org/abs/quant-ph/0312041 |
| DOI | 10.1142/S0217732304014197 |
| Journal | Mod. Phys. Lett. A, 19, No. 27, 2047 (2004). |
Abstract
We obtain the band edge eigenfunctions and the eigenvalues of solvable periodic potentials using the quantum Hamilton - Jacobi formalism. The potentials studied here are the Lam{\'e} and the associated Lam{\'e} which belong to the class of elliptic potentials. The formalism requires an assumption about the singularity structure of the quantum momentum function $p$, which satisfies the Riccati type quantum Hamilton - Jacobi equation, $ p^{2} -i \hbar \frac{d}{dx}p = 2m(E- V(x))$ in the complex $x$ plane. Essential use is made of suitable conformal transformations, which leads to the eigenvalues and the eigenfunctions corresponding to the band edges in a simple and straightforward manner. Our study reveals interesting features about the singularity structure of $p$, responsible in yielding the band edge eigenfunctions and eigenvalues.
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"abstract": "We obtain the band edge eigenfunctions and the eigenvalues of solvable\nperiodic potentials using the quantum Hamilton - Jacobi formalism. The\npotentials studied here are the Lam{\\\u0027e} and the associated Lam{\\\u0027e} which\nbelong to the class of elliptic potentials. The formalism requires an\nassumption about the singularity structure of the quantum momentum function\n$p$, which satisfies the Riccati type quantum Hamilton - Jacobi equation, $\np^{2} -i \\hbar \\frac{d}{dx}p = 2m(E- V(x))$ in the complex $x$ plane. Essential\nuse is made of suitable conformal transformations, which leads to the\neigenvalues and the eigenfunctions corresponding to the band edges in a simple\nand straightforward manner. Our study reveals interesting features about the\nsingularity structure of $p$, responsible in yielding the band edge\neigenfunctions and eigenvalues.",
"arxiv_id": "quant-ph/0312041",
"authors": [
"S. Sree Ranjani",
"A. K. Kapoor",
"P. K. Panigrahi"
],
"categories": [
"quant-ph"
],
"doi": "10.1142/S0217732304014197",
"journal_ref": "Mod. Phys. Lett. A, 19, No. 27, 2047 (2004).",
"title": "Calculation of Band Edge Eigenfunctions and Eigenvalues of Periodic Potentials through the Quantum Hamilton - Jacobi Formalism",
"url": "https://arxiv.org/abs/quant-ph/0312041"
},
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