  By constructing the commutative operators chain, we derive the integrable
conditions for solving the eigenfunctions of Dirac equation and Schr\"odinger
equation. These commutative relations correspond to the intrinsic symmetry of
the physical system, which are equivalent to the original partial differential
equation can be solved by separation of variables. Detailed calculation shows
that, only a few cases can be completely solved by separation of variables. In
general cases, we have to solve the Dirac equation and Schr\"odinger equation
by effective perturbation or approximation methods, especially in the cases
including nonlinear potential or self interactive potentials.
