Analytic Continuation of Eigenvalues of a Quartic Oscillator

We consider the Schrödinger operator on the real line with even quartic potential x 4 + α x 2 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 ar...

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Bibliographic Details
Published in:	Communications in mathematical physics Vol. 287; no. 2; pp. 431 - 457
Main Authors:	Eremenko, Alexandre, Gabrielov, Andrei
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer-Verlag 01.04.2009 Springer
Subjects:	Classical and Quantum Gravitation Complex Systems Exact sciences and technology Functions of a complex variable Mathematical analysis Mathematical and Computational Physics Mathematical methods in physics Mathematical Physics Mathematics Other topics in mathematical methods in physics Partial differential equations Physics Physics and Astronomy Quantum Physics Relativity Theory Sciences and techniques of general use Several complex variables and analytic spaces Theoretical Cell Decomposition Meromorphic Function Riemann Surface Analytic Continuation Anharmonic Oscillator Complex function Eigenvalues Eigenfunctions Analytic functions Analytic continuation Mathematical physics
ISSN:	0010-3616, 1432-0916
Online Access:	Get full text
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