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Nonlinear evolution equations associated with the Schrödinger spectral problem

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  • Jaworski, Marek

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.

Suggested Citation

  • Jaworski, Marek, 2017. "Nonlinear evolution equations associated with the Schrödinger spectral problem," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 105-109.
    • Handle: RePEc:eee:chsofr:v:100:y:2017:i:c:p:105-109
    DOI: 10.1016/j.chaos.2017.05.006
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