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Semi-Classical Approximation in Quantum Mechanics

Виктор Павлович Маслов, M. V. Fedoriuk

Springer eBooksJan 1, 19811,000 citations

Semi-classical approximations of Quantum Mechanical problems

Ulf O Karlsson

Jan 1, 20022 citations

On the semi-classical expansion in quantum mechanics for arbitrary Hamiltonians

Maurice M. Mizrahi

The purpose of this paper is to extend to a very wide class of Hamiltonians the range of validity of a well-known and oft-used expression for the semi-classical (WKB) approximation to the quantum-mechanical propagator K((q sub b),(t sub b);(q sub a),(t sub a)) identically equal to ((q sub a),(t sub b)/(q sub a),(t sub a)), or probability amplitude that a particle at (q sub a) at time (t sub a) will arrive at (q sub b) at time (t sub b).

May 1, 197637 citations

Propagators in quantum mechanics

Albino Hernández-Galeana, J. M. Rivera-Rebolledo, José Luis López-Bonilla +1 more

World Scientific NewsJan 1, 20180 citations

Quantum Mechanics and the Propagator

WORLD SCIENTIFIC eBooksOct 23, 20170 citations

Classical Mechanics in Hilbert Space: Path Integral Formulation, and a Quantum Correction

James Shee

While it is well-known that quantum mechanics can be reformulated in terms of a path integral representation, it will be shown that such a formulation is also possible in the case of classical mechanics. From Koopman-von Neumann theory, which recasts classical mechanics in terms of a Hilbert space wherein the Liouville operator acts as the generator of motion, we derive a path integral representation of the classical propagator and suggest an efficient numerical implementation using fast fourier transform techniques. We then include a first quantum correction to derive a revealing expression for the semi-classical path integral, which augments the classical picture of a single trajectory through phase space with additional wave-like spreading.While it is well-known that quantum mechanics can be reformulated in terms of a path integral representation, it will be shown that such a formulation is also possible in the case of classical mechanics. From Koopman-von Neumann theory, which recasts classical mechanics in terms of a Hilbert space wherein the Liouville operator acts as the generator of motion, we derive a path integral representation of the classical propagator and suggest an efficient numerical implementation using fast fourier transform techniques. We then include a first quantum correction to derive a revealing expression for the semi-classical path integral, which augments the classical picture of a single trajectory through phase space with additional wave-like spreading.

arXiv:1505.06391May 24, 20151 citation

On the semi-classical expression of the quantum-mechanical propagator

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