Path integral solution of the Schroedinger equation in curvilinear coordinates: A straightforward procedure

A new axiomatic formulation of path integrals is used to construct a path integral solution of the Schroedinger equation in curvilinear coordinates. An important feature of the formalism is that a coordinate transformation in the variables of the wavefunction does not imply a change of variable of integration in the path integral. Consequently, a transformation from Euclidean to curvilinear coordinates is simple to handle; there is no need to introduce open-quote open-quote quantum corrections close-quote close-quote into the action functional. Furthermore, the paths are differentiable: hence, issues related to stochastic paths do not arise. The procedure for constructing the path integral solution of the Schroedinger equation is straightforward. The case of the Schroedinger equation in spherical coordinates for a free particle is presented in detail. copyright 1996 American Institute of Physics