Correspondence rules and path integrals
A path-integral representation is constructed for propagators corresponding to quantum Hamiltonian operators obtained from classical Hamiltonians by an arbitrary rule of correspondence. Each rule yields a unique way of defining the path integral in the context of a formalism which does not require a limiting process. This formalism is more reliable than the usual time-slicing (lattice) definition in that all the expressions it entails are well-defined for computational purposes and it allows the explicit evaluation of large classes of path integrals. Direct substitution in the Schrödinger equation shows that there are no restrictions (such as Hermiticity or time-independence) on the Hamiltonian operator. Examples are given.
KeywordsQuantum Operator Hamiltonian Operator Correspondence Rule Arbitrary Rule Dinger Equation
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