Associated LamÉ Equation, Periodic Potentials and sl(2,R)

Details Associated LamÉ Equation, Periodic Potentials and sl(2,R) Associated LamÉ Equation, Periodic Potentials and sl(2,R)

2002-04-11

arxiv.org/abs/math-ph/0204026v1

Mod.Phys.Lett. A15 (2000) 1923

Physics

Mathematical Physics

8 pages, no figure, tex file(version 2.09)

Scientific paper

10.1142/S0217732300002346

We propose a new approach based on the algebraization of the Associated Lam\'{e} equation \[-\psi''(x) + [ m(m+1)k^{2}sn^{2}x + \ell(\ell+1)k^{2}(cn^{2}x/dn^{2}x)]\psi(x) = E\psi(x)\] within sl(2,R) to derive the corresponding periodic potentials. The band edge eigenfunctions and energy spectra are explicitly obtained for integers m,$\ell$. We also obtain the explicit expressions of the solutions for half-integer m and integer or half-integer $\ell$.

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