Spherical polar coordinates Laplace

Legendre s Associated Functions. We saw in example 1 of Chapter 1 that the solution of Laplace s equation in spherical polar coordinates reduces to the solution of the ordinary differential equation,... 

This equation can be solved by separation of variables, provided the potential is either a constant or a pure radial function, which requires that the Lapla-cian operator be specified in spherical polar coordinates. This transformation and solution of Laplace s equation, V2 / = 0, are well-known mathematical procedures, closely followed in solution of the wave equation. The details will not be repeated here, but serious students of quantum theory should familiarize themselves with the procedures [15]. 

The functions T , in spherical polar coordinates, appear as solutions to Laplace s equation of degree 1 ... 

Laplace s equation in spherical polar coordinates can be written as... 

Helmholtz s equation in spherical polar coordinates can be obtained by adding a constant to Laplace s equation (12.57) ... 

Here S Nft = 0 because of the electroneutrality condition.) Equation (1.3.10) is substituted into Eq. (1.3.6) and the Laplace operator is expressed in polar coordinates (for the spherically symmetric problem) ... 

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See also in sourсe #XX -- [ ]

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