Nonlinear evolution equations associated with the Schrödinger spectral problem

Marek Jaworski

Chaos, Solitons & Fractals, 2017, vol. 100, issue C, 105-109

Abstract: Evolution equations associated with the Schrödinger equation are derived for an arbitrary time-dependent potential. It is shown that the eigenvalues evolve according to the Hellmann–Feynman theorem, while the eigenfunction evolution can be determined either by solving a system of coupled differential equations or by a contour integration in the complex k-domain. A possible application to solving a class of Schrödinger spectral problems is also discussed.

Keywords: Lax pair; Schrödinger equation; Nonlinear evolution equations (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:100:y:2017:i:c:p:105-109

DOI: 10.1016/j.chaos.2017.05.006

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