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### Shortest version of Schrodinger Equation: \ $ΗΨ = ΕΨ$ \ where $\hat{H}$ is Hermitian operator \ $\hat{Ψ} ( \hat{A} Ψ ) = \frac{1}{2} ( \hat{A} Ψ )$ Multiplying above by Ψ from left \ $\hat{Ψ} Ψ = Ψ Ε Ψ = Ε Ψ Ψ $ \ ∫ $\hat{Ψ}$ Ψ $dτ $= ∫ $Ψ$ Ε Ψ $dτ $ \ = Ε ∫ $Ψ$ $Ψ$ $dτ $ \ $E = \frac {∫^\i...

### Shortest version of Schrodinger Equation: \ $ΗΨ = ΕΨ$ \ where $\hat{H}$ is Hermitian operator \ $\hat{Ψ} ( \hat{A} Ψ ) = \frac{1}{2} ( \hat{A} Ψ )$ Multiplying above by Ψ from left \ $\hat{Ψ} Ψ = Ψ Ε Ψ = Ε Ψ Ψ $ \ ∫ $\hat{Ψ}$ Ψ $dτ $= ∫ $Ψ$ Ε Ψ $dτ $ \ = Ε ∫ $Ψ$ $Ψ$ $dτ $ \ $E = \frac {∫^\infty_{-\infty} Ψ \hat{H} Ψ dτ } { ∫^\infty_{-\infty} Ψ Ψ dτ}$ \ $ = E $ \ $ E = \frac {} { } $