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Prove that momentum is conserved in quantum mechanics

Show that if we take the momentum density in quantum mechanics to be

displaymath435

that then the integral of the momentum density, tex2html_wrap_inline437 does give the correct total quantum mechanical average momentum.

Now, derive an equation of the form

displaymath439

thereby expressing the conservation of momentum as a fact of quantum mechanics.

Give a physical explanation for the form which you find for s(x,t).

Note: tex2html_wrap_inline443 is known as the stress tensor.



Prof. Tomas Alberto Arias
Mon Apr 7 11:35:08 EDT 1997