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As shown by Morse and Feshbach (1953) and Arfken (1970), the Helmholtz differential equation is separable in oblate spheroidal coordinates.

As shown by Morse and Feshbach (1953) and Arfken (1970), the Helmholtz differential equation is separable in prolate spheroidal coordinates.

As shown by Morse and Feshbach (1953), the Helmholtz differential equation is separable in confocal paraboloidal coordinates.

In elliptic cylindrical coordinates, the scale factors are h_u=h_v=sqrt(sinh^2u+sin^2v), h_z=1, and the separation functions are f_1(u)=f_2(v)=f_3(z)=1, giving a Stäckel ...

In parabolic cylindrical coordinates, the scale factors are h_u=h_v=sqrt(u^2+v^2), h_z=1 and the separation functions are f_1(u)=f_2(v)=f_3(z)=1, giving Stäckel determinant ...

In cylindrical coordinates, the scale factors are h_r=1, h_theta=r, h_z=1, so the Laplacian is given by del ...

An orthogonal coordinate system is a system of curvilinear coordinates in which each family of surfaces intersects the others at right angles. Orthogonal coordinates ...

A system for specifying points using coordinates measured in some specified way. The simplest coordinate system consists of coordinate axes oriented perpendicularly to each ...

Defined for a vector field A by (A·del ), where del is the gradient operator. Applied in arbitrary orthogonal three-dimensional coordinates to a vector field B, the ...

The azimuthal coordinate on the surface of a sphere (theta in spherical coordinates) or on a spheroid (in prolate or oblate spheroidal coordinates). Longitude is defined such ...