Supersymmetry and solvable periodic potentials

We use the formalism of supersymmetric quantum mechanics to enlarge considerably the limited class of analytically solvable one-dimensional periodic potentials. In particular, we derive and discuss the energy-band structure of the Lame potentials pm sn2(x, m) and associated Lame potentials pm sn2(x, m) + qm cn2(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 constitute even more new solvable potentials with exactly the same energy-band structure