Mathematical operators Laplacian

For an incompressible liquid (i.e. a liquid with an invariant density which implies that the mass balance at any point leads to div v = 0) the time dependency of the concentration is given by the divergence of the flux, as defined by equation (13). Mathematically, the divergence of the gradient is the Laplacian operator V2, also frequently denoted as A. Thus, for a case of diffusion and flow, equation (10) becomes ... 

This form of the equation is not easily applied to rotational motion because the Cartesian coordinates used do not reflect the centro-symmetric nature of the problem. It is better to express the Schrodinger equation in terms of the spherical polar coordinates r, 6 and 0, which are shown in Figure 5.7. Their mathematical relationship to x. y and z is given on the left of the diagram. In terms of these coordinates the Laplacian operator becomes ... 

According to mathematical analysis, the spatial operator utilized is called Laplacian and several notations are used ... 

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