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Indeed, in terms of [[spherical polar coordinates]] the operator is,

the operator ∇² expressed in [[spherical polar coordinates]], can be written as

where ''r'', θ, and φ are [[spherical polar coordinates]] of a point with respect to a system of axes centered on the central ion.

where θ and φ are the [[spherical polar coordinates|spherical polar angles]] of '''r''' with respect to a coordinate system in ...le-dipole interaction this is most easily proved by integrating over the [[spherical polar coordinates|spherical polar angles]] of the dipole vector, while using the volume eleme

* [[Spherical polar coordinates]]