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

Critical Missing Equation of Quantum Physics for Understanding Atomic Structures