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Generalized nonlinear Doebner-Goldin Schrödinger equation and the relaxation of quantum systems

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  • Dodonov, V.V.
  • Mizrahi, S.S.

Abstract

We propose a new class of nonlinear homogeneous extension of the Doebner-Goldin Schrödinger equation, valid for arbitrary representations and operators, chosen in accordance with the investigated physical problem. We verify that the nonlinearity simulates an environment, thence, the new model leads to simple exact solutions as, for instance, the time-dependent squeezed coherent states and a special class of stationary states that we call pseudothermal, reached after relaxation. We illustrate the use of the new equation with applications to problems such as, the relaxation of a two-level or spin-1/2 system, and of the harmonic oscillator (HO) or equivalently, the emission-absorption process of photons in an electromagnetic cavity. Furthermore, in order to compare solutions for the HO example we introduce two different representations in the new equation, one continuous (positional representation) and the other discrete (Fock states).

Suggested Citation

  • Dodonov, V.V. & Mizrahi, S.S., 1995. "Generalized nonlinear Doebner-Goldin Schrödinger equation and the relaxation of quantum systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 214(4), pages 619-628.
    • Handle: RePEc:eee:phsmap:v:214:y:1995:i:4:p:619-628
    DOI: 10.1016/0378-4371(94)00239-P
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    1. Syed Barakat Ahmad, 1973. "India and Palestine 1896–1947: The Genesis of a Foreign Policy," India Quarterly: A Journal of International Affairs, , vol. 29(4), pages 300-307, October.
    2. Mizrahi, Salomon S. & Marchiolli, Marcelo A., 1993. "Pseudo-diffusion equation and information entropy of squeezed-coherent states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 199(1), pages 96-115.
    3. Hayes, Kathy & Slottje, D. J. & Porter-Hudak, Susan & Scully, Gerald, 1990. "Is the size distribution of income a random walk?," Journal of Econometrics, Elsevier, vol. 43(1-2), pages 213-226.
    4. Popov, V.M. & Tataru, N.N. & Bajenesco, T.I., 1968. "Quelques solutions originales utilisees dans la construction d'une grande calculatrice analogique," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 10(4), pages 211-213.
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