The angular kinetic energy terms

The Legendre polynomials in cos 7 are eigenfunctions of the angular part of the kinetic energy expression, 

As our angular grid points we use the Gauss-Legendre quadrature points. The grid representation of the wavefunction, is 

There are two possible representations of the wavefunction. In the basis set representation, the wavefunction is expanded in terms of the Legendre polynomials, while the grid representation of the wavefunction is defined by eq. (5.7). We define the matrix U, which transforms the wavefunction from the basis set to the grid representation [4], 

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A more involved situation is found in curvilinear coordinates. For example, in circular coordinates the angular kinetic energy term T = (l/2mr2)(d2/dcj)2) correlates the angular kinetic energy with the radial coordinate r (Fig. 19). 

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