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Anharmonic oscillator discontinuity formulae up to second exponentially small order

Anharmonic oscillator discontinuity formulae up to second exponentially small order
Anharmonic oscillator discontinuity formulae up to second exponentially small order
The eigenvalues of the quartic anharmonic oscillator as functions of the anharmonicity constant satisfy a once-subtracted dispersion relation. In turn, this dispersion relation is driven by the purely imaginary discontinuity of the eigenvalues across the negative real axis. In this paper we calculate explicitly the asymptotic expansion of this discontinuity up to second-exponentially-small order.
0305-4470
4003-4016
Alvarez, Gabriel
5227cb90-72f6-4b7d-99ab-a3a7299f8ab2
Howls, Christopher J.
66d3f0f0-376c-4f7a-a206-093935e6c560
Silverstone, Harris J.
918b6a1a-9f33-4a7a-adb9-8ba64725f343
Alvarez, Gabriel
5227cb90-72f6-4b7d-99ab-a3a7299f8ab2
Howls, Christopher J.
66d3f0f0-376c-4f7a-a206-093935e6c560
Silverstone, Harris J.
918b6a1a-9f33-4a7a-adb9-8ba64725f343

Alvarez, Gabriel, Howls, Christopher J. and Silverstone, Harris J. (2002) Anharmonic oscillator discontinuity formulae up to second exponentially small order. Journal of Physics A: Mathematical and General, 35 (18), 4003-4016. (doi:10.1088/0305-4470/35/18/302).

Record type: Article

Abstract

The eigenvalues of the quartic anharmonic oscillator as functions of the anharmonicity constant satisfy a once-subtracted dispersion relation. In turn, this dispersion relation is driven by the purely imaginary discontinuity of the eigenvalues across the negative real axis. In this paper we calculate explicitly the asymptotic expansion of this discontinuity up to second-exponentially-small order.

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Published date: 2002
Organisations: Applied Mathematics

Identifiers

Local EPrints ID: 29215
URI: http://eprints.soton.ac.uk/id/eprint/29215
ISSN: 0305-4470
PURE UUID: 5af1d485-acc5-41f2-be2d-3264f05412fd
ORCID for Christopher J. Howls: ORCID iD orcid.org/0000-0001-7989-7807

Catalogue record

Date deposited: 11 May 2006
Last modified: 20 Jul 2019 01:08

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