Critical Missing Equation of Quantum Physics for Understanding Atomic Structures

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 Schrödinger 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

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