23
Coordinate Systems
Abstract
Coordinate systems play an important rôle in many areas of physics. Focus of
this chapter is coordinates for which the three dimensional Laplace–Beltrami
operator becomes separable. In detail 11 independent coordinate systems, plus
some important combinations and their mutual transformations will be discussed.
For completeness Jacobi coordinates and hyperspherical coordinates are added.
Related code for mutual transformations can be downloaded.
Coordinate systems play an important rôle in many areas of physics, e.g., in classical
dynamics, electrodynamics, and quantum dynamics to list only a few. Topics of this
chapter are coordinates for which the three dimensional Laplace–Beltrami operator
becomes separable. For applications we will focus on the Schrödinger equation.
Function Overview
sph2cart The MATLAB function sph2cart transforms spherical coordinates
to cartesian coordinates. The inverse transformation is given by the MATLAB
function cart2sph.
CoordTrafo The SPECFUNPHYS class CoordTrafo supports the transformation between all coordinate systems listed in Table 23.1.
Cone The SPECFUNPHYS function cone2c supports the transformation from
cone coordinates to cartesian coordinates.
Ellipsoidal The SPECFUNPHYS function edal2c supports the transformation
from ellipsoidal coordinates to cartesian coordinates.
d-spherical The SPECFUNPHYS function hyper2c supports the transformation from hyperspherical coordinates to cartesian coordinates, and the inverse
transformation from d-dimensional cartesian coordinates to hyperspherical coordinates is evaluated by the SPECFUNPHYS function c2hyper.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
W. Schweizer, Special Functions in Physics with MATLAB,
https://doi.org/10.1007/978-3-030-64232-7_23
259
Coordinate Systems
Abstract
Coordinate systems play an important rôle in many areas of physics. Focus of
this chapter is coordinates for which the three dimensional Laplace–Beltrami
operator becomes separable. In detail 11 independent coordinate systems, plus
some important combinations and their mutual transformations will be discussed.
For completeness Jacobi coordinates and hyperspherical coordinates are added.
Related code for mutual transformations can be downloaded.
Coordinate systems play an important rôle in many areas of physics, e.g., in classical
dynamics, electrodynamics, and quantum dynamics to list only a few. Topics of this
chapter are coordinates for which the three dimensional Laplace–Beltrami operator
becomes separable. For applications we will focus on the Schrödinger equation.
Function Overview
sph2cart The MATLAB function sph2cart transforms spherical coordinates
to cartesian coordinates. The inverse transformation is given by the MATLAB
function cart2sph.
CoordTrafo The SPECFUNPHYS class CoordTrafo supports the transformation between all coordinate systems listed in Table 23.1.
Cone The SPECFUNPHYS function cone2c supports the transformation from
cone coordinates to cartesian coordinates.
Ellipsoidal The SPECFUNPHYS function edal2c supports the transformation
from ellipsoidal coordinates to cartesian coordinates.
d-spherical The SPECFUNPHYS function hyper2c supports the transformation from hyperspherical coordinates to cartesian coordinates, and the inverse
transformation from d-dimensional cartesian coordinates to hyperspherical coordinates is evaluated by the SPECFUNPHYS function c2hyper.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
W. Schweizer, Special Functions in Physics with MATLAB,
https://doi.org/10.1007/978-3-030-64232-7_23
259