Classical mechanics, the diffusion (heat) equation, and the Schrödinger equation

Aubrey Truman

Research output: Contribution to journalArticle

Abstract

We consider the limiting case ??0 of the Cauchy problem (Equation Presented) u?(x,0) = exp[-S0(x)/?] T0(x); S0, T0 independent of ?, for both real and pure imaginary ?. We prove two new theorems relating the limiting solution of the above Cauchy problem to the corresponding equations of classical mechanics (Equation Presented) These relationships include the physical result quantum mechanics ? classical mechanics as ??0. Copyright © 1977 American Institute of Physics.

Original languageEnglish
Pages (from-to)2308-2315
Number of pages8
JournalJournal of Mathematical Physics
Volume18
Issue number12
Publication statusPublished - 1976

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