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FadeToBen
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Homework Statement
The problem asks me to find the expectation value of W.
Homework Equations
The given ψ[x,t] is Asin(πx/a) e^((-i Eot)/ħ).
By QM postulate 2 the QM operator of W is: iħ δ/δt or equivalently -ħ/i δ/δt.
The Attempt at a Solution
<w>=∫ψ*iħδ/δtψ= iħδ/δt 1/(2e^(-iEot/)ħ) sin(πx/a) e^(iEot/ħ) dx
I am trying to wrap my head around what is going on so far. Solving for A in the wave equation would require you to normalize and integrate. You then put the normalized wave function times the QM operator and solve for the expectation value. When solving for position this is no problemo. I hit a snag when solving for W and W^2. I thought that for energy you would be integrating with respect to time, which i was informed was incorrect.
We happened to glaze over this problem in class, but the time term from inside the wave function was brought out to cancel the partial wrt time.
I know that for my above attempt I messed up my U substitution pretty badly. I would just like some clarification on how the treatment of solving for W differs from position.
Thanks ahead of time helping this QM neophyte.