Assuming that V(x,y,z) can be expressed as V(x,y,z) = X(x)Y(y)Z(z) where X(x), Y(y) and Z(z) are functions of x, y and z respectively, we can write:

..............(2.117)

Dividing throughout by X(x)Y(y)Z(z) we get

.

In the above equation, all terms are function of one coordinate variably only, hence we can write:

 ...........................................................................(2.118)