Elliptic even finite-gap potentials and spectra of the Schrödinger operator

DOI

10.2991/jnmp.1995.2.2.8How to use a DOI?

Abstract

A simple method for calculating finite-gap elliptic potentials and corresponding spectra of the one-dimensional Schrödinger operator which is based on a general representation of the potentials in a form of rational functions of the Weierstrass function and trace formulae is proposed. It is shown that the 1-3-gap even elliptic potentials can be expressed only in a form of some linear combinations of the Lamé potentials with shifted arguments. The expressions for the 1-3-gap even elliptic potentials and corresponding spectral polynomials (the roots of which are spectrum boundaries) are obtained.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - A.M. Korostil'
PY  - 1995
DA  - 1995/05/01
TI  - Elliptic even finite-gap potentials and spectra of the Schrödinger operator
JO  - Journal of Nonlinear Mathematical Physics
SP  - 182
EP  - 192
VL  - 2
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1995.2.2.8
DO  - 10.2991/jnmp.1995.2.2.8
ID  - Korostil'1995
ER  -