Periodic Potentials and Supersymmetry

Details Periodic Potentials and Supersymmetry Periodic Potentials and Supersymmetry

2004-02-26

arxiv.org/abs/quant-ph/0402206v1

Physics

Quantum Physics

27 pages, 4 figures

Scientific paper

10.1088/0305-4470/37/43/002

We review the current status of one dimensional periodic potentials and also present several new results. It is shown that using the formalism of supersymmetric quantum mechanics, one can considerably enlarge the limited class of analytically solvable one-dimensional periodic potentials. Further, using the Landen transformations as well as cyclic identities for Jacobi elliptic functions discovered by us recently, it is shown that a linear superposition of Lam\'e (as well as associated Lam\'e) potentials are also analytically solvable. Finally, using anti-isospectral transformations, we also obtain a class of analytically solvable, complex, PT-invariant, periodic potentials having real band spectra.

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