  A general quantization rule for bound states of the Schrodinger equation is
presented. Like fundamental theory of integral, our idea is mainly based on
dividing the potential into many pieces, solving the Schr\"odinger equation,
and deriving the general quantization rule. For both exactly and non-exactly
solvable systems, the energy levels of all the bound states can be easily
calculated from the general quantization rule. Using this new general
quantization rule, we re-calculate the energy levels for the one-dimensional
system, with an infinite square well, with the harmonic oscillator potential,
with the Morse Potential, with the symmetric and asymmetric Rosen-Morse
potentials, with the first P\"oschl-Teller potential, with the Coulomb
Potential, with the V-shape Potential, and the ax^4 potential, and for the
three dimensions systems, with the harmonic oscillator potential, with the
ordinary Coulomb potential, and for the hydrogen atom.
