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Elsevier eBooks

Solution of the Schrödinger Equation in Spherical Coordinates

Published Jan 1, 2015• 0 citations
Publisher
DOI
10.1016/b978-0-12-800734-1.09972-8

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Comment on: Path integral solution of the Schrödinger equation in curvilinear coordinates: A straightforward procedure [J. Math. Phys. 37, 4310–4319 (1996)]

Alexander Wurm, J. LaChapelle

The authors comment on the paper by J. LaChapelle, J. Math. Phys. 37, 4310 (1996), and give explicit expressions for the parametrization, its solution, and the Lie derivatives of the Schrödinger equation for the case of n-dimensional spherical coordinates.

Journal of Mathematical Physics•May 1, 1997•0 citations

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

J. LaChapelle

A new axiomatic formulation of path integrals is used to construct a path integral solution of the Schrödinger 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 ‘‘quantum corrections’’ 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 Schrödinger equation is straightforward. The case of the Schrödinger equation in spherical coordinates for a free particle is presented in detail.

Journal of Mathematical Physics•Sep 1, 1996•0 citations
A new axiomatic formulation of path integrals is used to construct a path integral solution of the Schrödinger 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 ‘‘quantum corrections’’ 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 Schrödinger equation is straightforward. The case of the Schrödinger equation in spherical coordinates for a free particle is presented in detail.