From Maupertuis to Schrodinger. Quantization of classical variational principles

摘要

In his first paper on wave mechanics, Schrodinger presented a heuristic argument which led from the Hamilton-Jacobi equation through the quantum variational principle to his famous wave equation. In his second paper, Schrodinger withdrew this heuristic argument as "incomprehensible.'' We show by using a recently generalized form of Maupertuis' principle that Schrodinger's original heuristic argument can be made more logical. Aside from pedagogical interest, this path is useful as a method of quantization of general mechanical systems. (C) 1999 American Association of Physics Teachers. [References: 32]