Journal of Nonlinear Mathematical Physics

Volume 2, Issue 2, May 1995, Pages 182 - 192

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

Authors
A.M. Korostil'
Corresponding Author
A.M. Korostil'
Received 17 February 1995, Available Online 1 May 1995.
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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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
2 - 2
Pages
182 - 192
Publication Date
1995/05/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.1995.2.2.8How to use a DOI?
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/).

Cite this article

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  -