Periodic Potentials and Supersymmetry

Avinash Khare; Uday Sukhatme

doi:10.1088/0305-4470/37/43/002

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Periodic Potentials and Supersymmetry

Avinash Khare·Uday Sukhatme

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Abstract

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 Lamé (as well as associated Lamé) 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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Avinash Khare, Uday Sukhatme. 2004-02-26. Periodic Potentials and Supersymmetry. https://doi.org/10.1088/0305-4470/37/43/002

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