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The Hamilton-Jacobi theory and the analogy between classical and quantum mechanics

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  • 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.
    Mathematics Subject Classification: 70H20, 70S05, 70FXX, 70HXX.


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