Nodal properties of the scaled quartic anharmonic oscillator
type: Item
instance of: scholarly article
title: Nodal properties of the scaled quartic anharmonic oscillator
zbMATH Open document ID: 0646.58039
DOI: 10.1016/0003-4916(88)90004-8
author: Paul E. Shanley
published in: Annals of Physics
publication date: 1988-01-01T00:00:00Z
review text: The motions in the complex x-plane of the nodes, extrema, and turning points associated with the wavefunction \(\psi_ n(\gamma,x)\) of the scaled quartic anharmonic oscillator are studied when the quadratic coupling constant \(\gamma\) takes on complex values so as to produce level crossing. Nodal and extremal position functions are defined and their analytic properties in \(\gamma\) are studied together with those of the turning points. All functions are found to have a Riemann surface structure that may be related to that of the eigenvalues. A discussion is given of the possible application of the ideas developed to problems associated with quantum chaos.
Mathematics Subject Classification ID: 58Z05
Mathematics Subject Classification ID: 81S99
Mathematics Subject Classification ID: 58J50
zbMATH DE Number: 4054669
zbMATH Keywords: scaled quartic anharmonic oscillator
zbMATH Keywords: eigenvalues
MaRDI profile type: Publication
full work available at URL: 0003-4916(88)90004-8
OpenAlex ID: W4256108165
cites work: Spectral properties of the scaled quartic anharmonic oscillator
cites work: Q5570370
cites work: Quantal phase factors accompanying adiabatic changes
cites work: Q3279399
cites work: Pseudointegrable systems in classical and quantum mechanics
cites work: Quantising a generic family of billiards with analytic boundaries
cites work: The analytic structure of dynamical systems and self-similar natural boundaries
description: scientific article; zbMATH DE number 4054669