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Periodic Quasi - Exactly Solvable Models

S. Sree Ranjani·A. K. Kapoor·P. K. Panigrahi
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Abstract

Various quasi-exact solvability conditions, involving the parameters of the periodic associated Lam{é} potential, are shown to emerge naturally in the quantum Hamilton-Jacobi approach. It is found that, the intrinsic nonlinearity of the Riccati type quantum Hamilton-Jacobi equation is primarily responsible for the surprisingly large number of allowed solvability conditions in the associated Lam{é} case. We also study the singularity structure of the quantum momentum function, which yields the band edge eigenvalues and eigenfunctions.

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S. Sree Ranjani, A. K. Kapoor, P. K. Panigrahi. 2004-03-27. Periodic Quasi - Exactly Solvable Models. https://doi.org/10.1007/s10773-005-4436-0

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