  This paper presents an optimization approach to explain why and how a quantum
system evolves from an arbitrary initial state to a stationary state,
satisfying the time-independent Schr\"{o}dinger equation. It also points out
the inaccuracy of this equation, which is critial important in quantum
mechanics and quantum chemistry, due to a fundamental flaw in it conflicting
with the physical reality. The some directions are suggested on how to modify
the equation to fix the problem
