Quantum Hamilton-Jacobi equation
نویسنده
چکیده
The nontrivial transformation of the phase space path integral measure under certain discretized analogues of canonical transformations is computed. This Jacobian is used to derive a quantum analogue of the Hamilton-Jacobi equation for the generating function of a canonical transformation that maps any quantum system to a system with a vanishing Hamiltonian. A formal perturbative solution of the quantum Hamilton-Jacobi equation is given. A remarkable formulation of classical dynamics is provided by the Hamilton-Jacobi equation: If S(q; P; t) satis es
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