On a Path to Nonlinear Quantum Mechanics

H.-D. Doebner and J.-D. Hennig
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H.-D. Doebner: Technische Universität Clausthal, Arnold Sommerfeld Institut für Mathematische Physik
J.-D. Hennig: Technische Universität Clausthal, Arnold Sommerfeld Institut für Mathematische Physik

A chapter in Symmetries in Science IX, 1997, pp 81-92 from Springer

Abstract: 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 t 1 . 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.

Keywords: Pure State; Nonlinear Evolution; Nonlinear Evolution Equation; Schrodinger Equation; Nonlinear Schrodinger Equation (search for similar items in EconPapers)
Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4615-5921-4_6

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DOI: 10.1007/978-1-4615-5921-4_6

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