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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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