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In: Chemistry

3. Assume that a particle is confined to a box of length L, and that the...

3. Assume that a particle is confined to a box of length L, and that the system wave function is

ψ(x)=sqrt(2/L)*sin[(π*x)/(L)]
(1) Is this state an eigenfunction of the momentum operator? Show your work.
(2) Calculate the average value of the momentum <p> that would be obtained for a large number of measurements. Explain your result.
(3) Calculate the probability that the particle is found between 0.31 L and 0.35 L.

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