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Time-dependent form

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Annotated LaTeXWrap leaf terms with \htmlData{term=key}{...}. Nested terms are refused.
iℏ∂Ψ∂t=H^Ψ\htmlData{term=imaginary-unit}{i} \htmlData{term=reduced-planck}{\hbar} \frac{ \partial \htmlData{term=wavefunction}{\Psi} }{ \partial \htmlData{term=time}{t} } = \htmlData{term=hamiltonian}{\hat{H}} \htmlData{term=wavefunction}{\Psi}
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Definition

i2=−1i^2=-1. It makes the generator of time evolution unitary rather than dissipative.

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Role

Turns the Hamiltonian into a phase rotation of Ψ\Psi. Without ii, probability would not be conserved.

Effect

The factor ii is why stationary states pick up a phase e−iEt/ℏe^{-iEt/\hbar} instead of growing or decaying.

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