The Hamilton--Jacobi Theory and the Analogy between Classical and Quantum Mechanics

Details The Hamilton--Jacobi Theory and the Analogy between Classical and Quantum Mechanics The Hamilton--Jacobi Theory and the Analogy between Classical and Quantum Mechanics

2009-07-06

arxiv.org/abs/0907.0964v1

Physics

Mathematical Physics

42 pages, LaTeX with AIMS class

Scientific paper

We review here some conventional as well as less conventional aspects of the time-independent and time-dependent Hamilton-Jacobi (HJ) theory and of its connections with Quantum Mechanics. Less conventional aspects involve the HJ theory on the tangent bundle of a configuration manifold, the quantum HJ theory, HJ problems for general differential operators and the HJ problem for Lie groups.

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