On the convergence of quantum resonant-state expansion

J. M. Brown; P. Jakobsen; A. Bahl; J. V. Moloney; M. Kolesik

doi:10.1063/1.4944625

On the convergence of quantum resonant-state expansion

J. M. Brown
, P. Jakobsen
, A. Bahl
, J. V. Moloney
, M. Kolesik

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

Completeness of the system of Stark resonant states is investigated for a one-dimensional quantum particle with the Dirac-delta potential exposed to an external homogeneous field. It is shown that the resonant series representation of a given wavefunction converges on the negative real axis while the series diverges on the positive axis. Despite the divergent nature of the resonant expansion, good approximations can be obtained in a compact spatial domain.

Original language	English (US)
Article number	032105
Journal	Journal of Mathematical Physics
Volume	57
Issue number	3
DOIs	https://doi.org/10.1063/1.4944625
State	Published - Mar 1 2016

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.4944625

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title = "On the convergence of quantum resonant-state expansion",

abstract = "Completeness of the system of Stark resonant states is investigated for a one-dimensional quantum particle with the Dirac-delta potential exposed to an external homogeneous field. It is shown that the resonant series representation of a given wavefunction converges on the negative real axis while the series diverges on the positive axis. Despite the divergent nature of the resonant expansion, good approximations can be obtained in a compact spatial domain.",

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AU - Brown, J. M.

AU - Jakobsen, P.

AU - Bahl, A.

AU - Moloney, J. V.

AU - Kolesik, M.

PY - 2016/3/1

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N2 - Completeness of the system of Stark resonant states is investigated for a one-dimensional quantum particle with the Dirac-delta potential exposed to an external homogeneous field. It is shown that the resonant series representation of a given wavefunction converges on the negative real axis while the series diverges on the positive axis. Despite the divergent nature of the resonant expansion, good approximations can be obtained in a compact spatial domain.

AB - Completeness of the system of Stark resonant states is investigated for a one-dimensional quantum particle with the Dirac-delta potential exposed to an external homogeneous field. It is shown that the resonant series representation of a given wavefunction converges on the negative real axis while the series diverges on the positive axis. Despite the divergent nature of the resonant expansion, good approximations can be obtained in a compact spatial domain.

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On the convergence of quantum resonant-state expansion

Abstract

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