Asymptotics of the eigenvalues of the rotating harmonic oscillator
type: Item
instance of: scholarly article
title: Asymptotics of the eigenvalues of the rotating harmonic oscillator
zbMATH Open document ID: 0928.34063
DOI: 10.1016/S0377-0427(98)00070-3
author: T. M. Dunster
published in: Journal of Computational and Applied Mathematics
publication date: 2000-01-12T00:00:00Z
review text: The asymptotic theory of the radial Schrödinger equation \[ {d^2 w\over dr^2}= \left({(1-r)^2 \over 4\alpha^2}- {\lambda+ {1\over 2} \over \alpha}+ {l(l+1) \over r^2} \right)w \] was developed to find an approximation for the eigenvalues of \(\lambda_N\), which are recessive at both \(r=0\) and \(r=+ \infty\). If there the coupling parameter \(\alpha\) is small, asymptotic expansions are given for \(\lambda\). This approximation consists of two components: an asymptotic expansion in powers of \(\alpha\) and a single term which is exponentially small. The Liouville transformation is required to derive the approximation, the Liouville-Green approximation for an expansion in unbounded domains, the effect of the exponentially small term, and an approximation valid at \(r=0\) (the modified Bessel function is used) are described.
Mathematics Subject Classification ID: 34L20
Mathematics Subject Classification ID: 81Q10
Mathematics Subject Classification ID: 34L40
Mathematics Subject Classification ID: 34E20
Mathematics Subject Classification ID: 81Q05
zbMATH DE Number: 1326349
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: WKB methods
zbMATH Keywords: turning point theory
zbMATH Keywords: solutions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1326349