Title

Analytic continuation of eigenvalues of a quartic oscillator

Abstract

We consider the Schrödinger operator on the real line with even quartic potential x4 + α x2 and study analytic continuation of eigenvalues, as functions of parameter α. We prove several properties of this analytic continuation conjectured by Bender, Wu, Loeffel and Martin. 1. All eigenvalues are given by branches of two multi-valued analytic functions, one for even eigenfunctions and one for odd ones. 2. The only singularities of these multi-valued functions in the complex α-plane are algebraic ramification points, and there are only finitely many singularities over each compact subset of the α-plane. [ABSTRACT FROM AUTHOR].

Keywords

EIGENVALUES, MATRICES, NONLINEAR oscillators

Date of this Version

2009

DOI

10.1007/s00220-008-0663-6

Volume

287

Issue

2

Pages

431-457

Link Out to Full Text

http://web.ebscohost.com/ehost/detail?sid=4e44a5e7-fb56-4414-a561-41148d27d1ec%40sessionmgr4&vid=1&hid=24&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#db=mth&AN=36649764