On the global existence of Bohmian mechanics
Copyright policy )On the global existence of Bohmian mechanics
We show that the particle motion in Bohmian mechanics, given by the solution of an ordinary differential equation, exists globally: For a large class of potentials the singularities of the velocity field and infinity will not be reached in finite time for typical initial values. A substantial part of the analysis is based on the probabilistic significance of the quantum flux. We elucidate the connection between the conditions necessary for global existence and the self-adjointness of the Schrödinger Hamiltonian.
35 pages, LaTex
- University of Genoa Italy
- Rutgers, The State University of New Jersey United States
- University of Padua Italy
- Rutgers University New Brunswick United States
- Ludwig-Maximilians-Universität München Germany
equation of D. Bohm's mechanics, Quantum Physics, hydrodynamic interpretation of the probability density, Applications of operator theory in the physical sciences, Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.), 81P15, FOS: Physical sciences, Schrödinger equation, Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory, Foundations of Quantum Mechanics; Bohmian mechanics; Functional analysis, 81S20, 81P20, 47N50, Quantum Physics (quant-ph), Selfadjoint operator theory in quantum theory, including spectral analysis
equation of D. Bohm's mechanics, Quantum Physics, hydrodynamic interpretation of the probability density, Applications of operator theory in the physical sciences, Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.), 81P15, FOS: Physical sciences, Schrödinger equation, Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory, Foundations of Quantum Mechanics; Bohmian mechanics; Functional analysis, 81S20, 81P20, 47N50, Quantum Physics (quant-ph), Selfadjoint operator theory in quantum theory, including spectral analysis
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