PHASE-SPACE PATH INTEGRATION OF INTEGRABLE QUANTUM-SYSTEMS

A new method for exact evaluation of phase space path integrals for integrable quantum systems is presented. By making use of point canonical and other transformations to bring the Hamiltonian to a form linear in the coordinates, the path integral is changed so that the functional q integration may be done. This produces a momentum delta functional which can be evaluated to give an ordinary integral. This procedure is applied to find an expression for the exact propagator for a particle in the harmonic oscillator potential, the inverse quadratic potential, the Coulomb potential, the Morse potential, the 1 cosh2(x) potential, and for a free particle propagating on the 2-sphere. The latter two problems are solved for the first time wholly within the path integral formalism. © 1990.