PATH INTEGRAL SOLUTION FOR A PARTICLE CONFINED IN A REGION

The propagator relative to a particle constrained to move in a finite region of space is calculated in the framework of path integrals. This region of the three-dimensional space is delimited through a sector of opening angle α, and also through the action of two attractive harmonic potentials, one being central and located in the Oxy plan, and the other directed along the z axis, with respective pulsations ω and ω0. It is shown that for α = π/2 and π the propagator is the sum of propagators evaluated on classical paths. The important case of the edge (α = 2π) is considered. © 1990 American Institute of Physics.