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``Classical'' Propagator and Path Integral in the Probability Representation of Quantum Mechanics

1999/03/01 by Olga Man'ko, Olga V. Man’ko, Man'ko, Olga +3
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Radioactive Decay and Measurement Techniques #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/9903002

LATEX,10 pages,accepted by Journal of Russian Laser Research,1999

arxiv created 1999/03/01 · openalex publication_date 1999/03/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the probability representation of the standard quantum mechanics, the explicit expression (and its quasiclassical van-Fleck approximation) for the ``classical'' propagator (transition probability distribution), which completely describes the quantum system's evolution, is found in terms of the quantum propagator. An expression for the ``classical'' propagator in terms of path integral is derived. Examples of free motion and harmonic oscillator are considered. The evolution equation in the Bargmann representation of the optical tomography approach is obtained.

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