Problem 3 in the continuous systems and fields chapter of (the first edition, 1956 printing) of Goldstein's classical mechanics has the following Lagrangian:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

L = \frac{h^2}{8 \pi^2 m} \nabla \psi \cdot \nabla \psi^{*}

+ V \psi \psi^{*}

+ \frac{h}{2\pi i}

( \psi^{*} \dot{\psi}

- \psi \dot{\psi}^{*} )

[/tex]

The problem is to treat [itex]\psi[/itex] and its conjugate as independent field variables and show that this generates Schodinger's equation and its conjugate.

Doing the problem I find I need [itex]h/4\pi i[/itex] in this last term to make it work out. Could somebody with a newer edition of this text see if this is a corrected typo?

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# Goldstein schodinger's equation Lagragian problem.

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