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Hamiltonian Operator in Generalized Coordinates

1965; American Institute of Physics; Volume: 33; Issue: 11 Linguagem: Inglês

10.1119/1.1971067

1943-2909

Lionel D. Dureau,

Quantum chaos and dynamical systems

The quantum mechanical, time-dependent wave equation in generalized coordinates is obtained by a slight modification of Schrödinger's original derivation. If the classical Hamiltonian for a system is known, the variational technique may be applied to the Hamilton-Jacobi equation to yield an Euler-Lagrange equation. This latter is then the wave equation for the system. The method, which is generally easy to apply, is illustrated by applications to a single particle in curvilinear coordinates and to a symmetric top molecule.