Abstract
We discuss how supersymmetric quantum mechanics can be used to enlarge the class of analytically solvable one-dimensional periodic potentials. We obtain the energy band structure of the Lame potentials pmsn2(x, m) and associated Lame potentials pmsn2(x, m) + qmcn2(x, m)/dn2 (x, m), both of which involve Jacobi elliptic functions with modulus parameter m. We find several new analytic expressions for band edge energies and wave functions. The supersymmetric partners of Lame and associated Lame potentials are additional new solvable potentials with richer spatial features but exactly the same energy band structure.
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