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

Maurice M. Mizrahi

Open publisher page 37 citations

Abstract

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).

About this research paper

What this paper is about

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).

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OpenAlex reports 37 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

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).

Key concepts: Physics, Classical mechanics, Quantum mechanics, Theoretical physics, Mathematics

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