1999/06/14 by Avinash Khare, Uday Sukhatme, U. Sukhatme · 4 citations
Chemistry · Mathematics · Physics and Astronomy · #Class (philosophy) #Computation #Computer science #Formalism (music) #Integer (computer science) #Mathematical physics #Mathematics #Periodic potential #Physics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Quantum statistical mechanics #Supersymmetric quantum mechanics #Supersymmetry #Synthesis and Properties of Aromatic Compounds #cond-mat #hep-th #quant-ph
paper · pdf · doi:10.1063/1.533040
published as J.Math.Phys. 40 (1999) 5473-5494 · 24 pages and 10 figures
arxiv created 1999/06/14 · openalex publication_date 1999/11/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Using the formalism of supersymmetric quantum mechanics, we obtain a large number of new analytically solvable one-dimensional periodic potentials and study their properties. More specifically, the supersymmetric partners of the Lamé potentials ma(a+1)sn2(x,m) are computed for integer values a=1,2,3,… . For all cases (except a=1), we show that the partner potential is distinctly different from the original Lamé potential, even though they both have the same energy band structure. We also derive and discuss the energy band edges of the associated Lamé potentials pm sn2(x,m)+qm cn2(x,m)/dn2(x,m), which constitute a much richer class of periodic problems. Computation of their supersymmetric partners yields many additional new solvable and quasiexactly solvable periodic potentials.