2003/12/04 by S. Sree Ranjani, A. K. Kapoor, P. K. Panigrahi +1
Chemistry · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #quant-ph
paper · pdf · doi:10.1142/s0217732304014197
published as Mod. Phys. Lett. A, 19, No. 27, 2047 (2004). · 21 pages, 5 tables
arxiv created 2003/12/04 · openalex publication_date 2004/08/30 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We demonstrate the procedure of finding the band edge eigenfunctions and eigenvalues of periodic potentials, through the quantum Hamilton–Jacobi formalism. The potentials studied here are the Lamé and associated Lamé, which belong to the class of elliptic potentials. The formalism requires an assumption about the singularity structure of the quantum momentum function p, obeying a Riccati type equation in the complex x-plane. Essential use is made of suitable conformal transformations, which lead to the eigenvalues and the eigenfunctions corresponding to the band edges, in a straightforward manner. Our study reveals interesting features about the singularity structure of p, underlying the band edge states.