Avinash Khare and Uday Sukhatme 2004 J. Phys. A: Math. Gen. 37 10037 doi:10.1088/0305-4470/37/43/002
Avinash Khare1 and Uday Sukhatme2
Show affiliationsWe 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 is 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.
03.65.Ge Solutions of wave equations: bound states
Issue 43 (29 October 2004)
Received 20 February 2004, in final form 14 May 2004
Published 14 October 2004
Avinash Khare and Uday Sukhatme 2004 J. Phys. A: Math. Gen. 37 10037
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