to separate the variables. To circu

to separate the variables. To circumvent this problem, a change of coordinates to polar coordinates is
made. After that is done, the Laplacian must be transformed into polar coordinates, which is a tedious
task. When the transformation is made, the variables can be separated so that three second-order differential equations, each containing one coordinate as the variable, are obtained. Even after this is done,
the resulting equations are quite complex, and the solution of two of the three equations requires the
use of series techniques. The solutions are described in detail in most quantum mechanics books, so
it is not necessary to solve the equations here (see suggested readings at the end of this chapter), but
Table 2.2 shows the wave functions. These wave functions are referred to as hydrogen-like wave functions
because they apply to any one-electron system (e.g., He , Li 2 ).