Standard quantum mechanics featuring probabilities instead of wave functions

Journal Article · Thu Jun 15 00:00:00 EDT 2006 · Physics of Atomic Nuclei

DOI:https://doi.org/10.1134/S1063778806060172· OSTI ID:21076043

Manko, V. I., E-mail: [e-mail]; Manko, O. V. ^[1]

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1. Russian Academy of Sciences, Lebedev Institute of Physics (Russian Federation), E-mail: [e-mail]

A new formulation of quantum mechanics (probability representation) is discussed. In this representation, a quantum state is described by a standard positive definite probability distribution (tomogram) rather than by a wave function. An unambiguous relation (analog of Radon transformation) between the density operator and a tomogram is constructed both for continuous coordinates and for spin variables. A novel feature of a state, tomographic entropy, is considered, and its connection with von Neumann entropy is discussed. A one-to-one map of quantum observables (Hermitian operators) on positive probability distributions is found.

• OSTI ID: 21076043
• Journal Information: Physics of Atomic Nuclei, Vol. 69, Issue 6; Other Information: DOI: 10.1134/S1063778806060172; Copyright (c) 2006 Nauka/Interperiodica; Article Copyright (c) 2006 Pleiades Publishing, Inc; Country of input: International Atomic Energy Agency (IAEA); ISSN 1063-7788
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
DENSITY
DISTRIBUTION
ENTROPY
HERMITIAN OPERATORS
PROBABILITY
QUANTUM MECHANICS
SPIN
WAVE FUNCTIONS