PATH-INTEGRAL SOLUTION OF THE SCHRODINGER-EQUATION IN CURVILINEAR COORDINATES - A STRAIGHTFORWARD PROCEDURE

A new axiomatic formulation of path integrals is used to construct a p ath integral solution of the Schrodinger equation in curvilinear coord inates. An important feature of the formalism is that a coordinate tra nsformation in the variables of the wavefunction does not imply a chan ge of variable of integration in the path integral. Consequently, a tr ansformation from Euclidean to curvilinear coordinates is simple to ha ndle; there is no need to introduce ''quantum corrections'' into the a ction functional. Furthermore, the paths are differentiable: hence, is sues related to stochastic paths do not arise. The procedure for const ructing the path integral solution of the Schrodinger equation is stra ight forward. The: case of the Schrodinger equation in spherical coord inates for a free particle is presented in detail. (C) 1996 American I nstitute of Physics.