The Hamilton-Jacobi theory and the analogy between classical and
Giuseppe Marmo - Dipartimento di Scienze Fisiche and INFN, Università di Napoli "Federico II". v. Cintia. I-80126 Naples, Italy (email)
Abstract: 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.
Keywords: Hamilton-Jacobi equation, Lagrangian system, Hamiltonian system, Semiclassical Approximation.
Received: February 2009; Revised: April 2009; Available Online: November 2009.
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