Abstract
Various quasi-exact solvability conditions, involving the parameters of the periodic associated Lamé potential, are shown to emerge naturally in the quantum Hamilton–Jacobi (QHJ) approach. We study the singularity structure of the quantum momentum function, which yields the band-edge eigenvalues and eigenfunctions and compare it with the solvable and quasi-exactly solvable non-periodic potentials, as well as the periodic ones.
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References
Atre, R. and Panigrahi, P. K. (2003). Physics Letter A 317, 46.
Arscot, F. M. (1964). Periodic Differential Equations, Pergamon, Oxford.
Dunne, G. V. and Fienberg, J. (1998). Physical Review D 57, 1271.
Ganguly, A. (2002). Journal of Mathematical Physics 43, 1980.
Geogo, K. G., Sree Ranjani, S., and Kapoor, A. K. (2003). Journal of Physics A: Mathematical and General 36, 4591.
González-López, A., Kamran, N., and Olver, P. J. (1991). Journal of Physics A: Mathematical and General 24, 3995.
Hancock, H. (1958). Theory of Elliptic Functions, Dover, New York.
Khare, A. and Sukhatme, U. (1999). Journal of Mathematical Physics 40, 5473.
Khare, A. and Sukhatme, U. (2001). Journal of Mathematical Physics 42, 5652.
Leacock, R. A. and Padgett, M. J. (1983). Physical Review Letters 50, 3.
Leacock, R. A. and Padgett, M. J. (1983). Physical Review D 28, 2491.
Magnus, W. and Wrinkler, S. (1966). Hills Equation, Inter Science, New York.
Razavy, M. (1980). American Journal of Physics 48, 285.
Razavy, M. (1981). Physics Letters A 82, 7.
Shifman, M. A. (1989). International Journal of Modern Physics A 4, 2897, and references therein.
Singh, V., Biswas, S. N., and Datta, K. (1978). Physical Review D 18, 1901.
Sree Ranjani, S., Kapoor, A. K., and Panigrahi, P. K. (2004). Modern Physics Letters A 19, 2047.
Tkachuk, V. M. and Voznyak, O. (2002). Physics Letters A 301, 177.
Turbiner, A. V. and Ushveridze, A. (1987). Physics Letters A 126, 181.
Ushveridze, A. (1994). Quasi-Exactly Solvable Models in Quantum Mechanics, Inst. of Physics Publishing, Bristol, and references therein.
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Ranjani, S.S., Kapoor, A.K. & Panigrahi, P.K. Periodic Quasi-Exactly Solvable Models. Int J Theor Phys 44, 1167–1176 (2005). https://doi.org/10.1007/s10773-005-4436-0
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DOI: https://doi.org/10.1007/s10773-005-4436-0