Physics of Atomic Nuclei

Standard quantum mechanics featuring probabilities instead of wave functions

Vladimir I. Man’ko, Olga V. Man’ko

Published Jun 1, 2006• 6 citations

Abstract

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.

DOI: 10.1134/s1063778806060172

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