Quantization via Classical Orbits
نویسنده
چکیده
A systematic method for calculating higher-order corrections of the relativistic semiclassical fixed-energy amplitude is given. The central scheme in computing corrections of all orders is related to a time ordering operation of an operator involving the Van Vleck determinant. This study provides us a new viewpoint for quantization. PACS 03.20.+i; 04.20.Fy; 02.40.+m Typeset using REVTEX ∗e-mail: [email protected] 1 I. CORRECTION OF ALL ORDER FOR THE SEMICLASSICAL RELATIVISTIC FIXED-ENERGY AMPLITUDE It was pointed out by Van Vleck [1] that the semiclassical approximation of the propagator in quantum mechanics can be expressed via the superposition of terms involving the classical action in the exponent, and allowing for more than one possible classical paths between two specified points in a given time interval (tb − ta): Ksc(xb,xa; tb − ta) = ∑ classical orbit ( M 2πh̄i )D/2 √
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