- #1

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the attachment shows my work. I honestly think maybe i did something wrong. at any rate the integrand is 1 and so not really even or odd.

any help is appreciated

- Thread starter watanake
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- #1

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the attachment shows my work. I honestly think maybe i did something wrong. at any rate the integrand is 1 and so not really even or odd.

any help is appreciated

- #2

gabbagabbahey

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Where did the integral in your first step come from? Start with the definition of [itex]\langle \hat{P} \rangle[/itex]...View attachment 51114

the attachment shows my work. I honestly think maybe i did something wrong. at any rate the integrand is 1 and so not really even or odd.

any help is appreciated

- #3

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So would be <p> =∫ψ*(x)P(hat)ψ(x)dx

P(hat) = -ih(bar)(d/dx)

- #4

gabbagabbahey

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The average linear momentum of

So would be <p> =∫ψ*(x)P(hat)ψ(x)dx

P(hat) = -ih(bar)(d/dx)

Remember, [itex]\psi_k(x)=e^{ikx}[/itex] is just one k-mode of the full wavefunction for a free particle [itex]\psi(x)=\int_{-\infty}^{\infty} A(k) \psi_k(x)dk [/itex].

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- #6

gabbagabbahey

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Does [itex]\frac{\infty}{\infty}=1[/itex]? That is essentially what you are claiming in your last step.

As for your first step, is that the definition of average momentum you are using in your course? Usually one defines the expectation value, or average, of an operator [itex]\hat{A}[/itex] in a given state [itex]|\psi\rangle[/itex] as [itex]\langle \hat{A} \rangle \equiv \langle \psi |\hat{A}|\psi \rangle[/itex].

Frankly, I'm still not 100% clear on what the original problem is. Can you post the original problem verbatim (word for word)?

- #7

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Also, [; <p>= m\frac{d<x>}{dt} ;], so if you can find [;<x>;], you should also be able to find [;<p>;].