A formalism that utilizes the analytic transfer matrix technique is applied
to the Schrodinger equation. This approach leads to proofs that the phase
loss at a turning point is exactly equal to pi. We also show the existence
of the phase contributions devoted by the scattered subwaves, which to our
knowledge, have never been taken into account in previous works. Subsequent
ly, an exact quantization condition, which differs essentially from the WKB
method, is introduced for arbitrary potential wells.