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On a Path to Nonlinear Quantum Mechanics

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Symmetries in Science IX

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Abstract

Quantum mechanics is an intrinsically linear theory. Its mathematical framework is based on three related building blocks. We consider a system localized on a smooth (finite dimensional) space-manifold M moving (non-relativistically) with time t; the physical space-time is M x R 1t . The following building blocks are modeled on a separable Hilbert space Н chosen as L 2(M, dμ) with elements depending on t: (1) Observables — for fixed t — are given by elements A of the set SA(Н) of (linear) self-adjoint operators. The spectral representation allows a probability interpretation of the observables.

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Author information

Authors and Affiliations

  1. Arnold Sommerfeld Institut für Mathematische Physik, Technische Universität Clausthal, D-38678, Clausthal-Zellerfeld, Germany

    H.-D. Doebner & J.-D. Hennig

Authors
  1. H.-D. Doebner
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  2. J.-D. Hennig
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Editor information

Editors and Affiliations

  1. Southern Illinois University at Carbondale, Carbondale, Illinois, USA

    Bruno Gruber

  2. Technische Universität Graz, Graz, Austria

    Michael Ramek

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Doebner, HD., Hennig, JD. (1997). On a Path to Nonlinear Quantum Mechanics. In: Gruber, B., Ramek, M. (eds) Symmetries in Science IX. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5921-4_6

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  • DOI: https://doi.org/10.1007/978-1-4615-5921-4_6

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7715-3

  • Online ISBN: 978-1-4615-5921-4

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