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    Action functionals for the time-dependent and stationary Schrödinger equations

    P-TRIV-VP12

    Area
    Prelim
    Status
    draft
    Contents

    Construct the functional \(S [ \psi , \psi ^ { \dagger } ]\) whose variation with respect to \(\psi = \psi ( \vec { r } , t )\) and \(\psi ^ { \dagger } = \psi ^ { \dagger } ( \vec { r } , t )\) gives

    1. the Schrodinger equation \(i \hbar \frac { \partial \psi } { \partial t } = \hat { H } \psi\) and its conjugated,

    2. the stationary Schrodinger equation \({ \hat { H } } \psi = E \psi\) and its conjugated.

    Here \(\hat { H }\) is some hermitian operator.

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