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Homework Statement
What will momentum measurement of a particle whose wave  function is given by ## \psi = e^{i3x} + 2e^{ix} ## yield?
Sketch the probability distribution of finding the particle between x = 0 to x = 2π.
Homework Equations
The Attempt at a Solution
The eigenfunctions of momentum operator is given by ## A e^{ikx}## where k = ## \frac p {\hbar} ## with eigen value p = ## {\hbar} k##.
Thus eigenvalue of ##e^{i3x}## is ## 3 \hbar ## and ##e^{ix}## is ## \hbar ##. I feel myself tempted to take the eigenvalues of momentum operator to be discrete and say that the momentum measurement will be either ## 3 \hbar ## or ## \hbar ##.
As the eigenvalue of momentum operator is continuous, I should use equation. (3.56) to answer the question.
Assuming that the question asks to calculate the probability distribution at t = 0, probability density would be given by ##  \psi ^2 = 3 + 2 ( e^{ i2x} +e^{i2x} )##., a complex function. But, the probability density should be a real valued function.
Is this correct?
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