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Exact wave functions for generalized harmonic oscillators

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Journal of Russian Laser Research Aims and scope

Abstract

We transform the time-dependent Schrödinger equation for the most general variable quadratic Hamiltonians into a standard autonomous form. As a result, the time evolution of exact wave functions of generalized harmonic oscillators is determined in terms of the solutions of certain Ermakov and Riccatitype systems. In addition, we show that the classical Arnold transform is naturally connected with Ehrenfest’s theorem for generalized harmonic oscillators.

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Authors and Affiliations

  1. School of Mathematical & Statistical Sciences, Arizona State University, Tempe, AZ, 85287-1904, USA

    Nathan Lanfear & Sergei K. Suslov

  2. Mathematical & Computational Modeling Sciences Center, Arizona State University, Tempe, AZ, 85287-1804, USA

    Raquel M. López & Sergei K. Suslov

Authors
  1. Nathan Lanfear
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  2. Raquel M. López
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  3. Sergei K. Suslov
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Correspondence to Sergei K. Suslov.

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Lanfear, N., López, R.M. & Suslov, S.K. Exact wave functions for generalized harmonic oscillators. J Russ Laser Res 32, 352–361 (2011). https://doi.org/10.1007/s10946-011-9223-1

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  • DOI: https://doi.org/10.1007/s10946-011-9223-1

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