TL;DR
This paper derives a quantum analogue of the Hamilton-Jacobi equation using path integral measure transformations, providing a formal perturbative solution and exploring canonical transformations in quantum systems.
Contribution
It introduces a quantum Hamilton-Jacobi equation derived from path integral measure transformations and offers a perturbative solution for quantum canonical transformations.
Findings
Derived the Jacobian for phase space path integral measure transformations.
Formulated a quantum Hamilton-Jacobi equation for generating functions.
Provided a formal perturbative solution to the quantum Hamilton-Jacobi equation.
Abstract
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.
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