On the Semi-Classical Expansion in Quantum Mechanics for Arbitrary Hamiltonians,

摘要

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).