What are the expectation values for position and momentum in states Ψ0 and Ψ1?

[Somali_Physicist]

Homework Statement

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Relevant Equations

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For question 2.2:

<Ψ₀|p|Ψ₀> = ∫Ψ₀ -iħ d/dx(Ψ₀) =M

Using Integration by parts i get:

M = -Ψ₀ iħ d/dx(Ψ₀) (assuming hilbert space)

Implying the expectation values for momentum are zero , however i get all the expectation values are zero for x and momentum in both states which makes no sense :(

 

[PeroK]

Homework Statement: Look Below Picture
Homework Equations: Look in Picture

View attachment 248596

For question 2.2:

<Ψ₀|p|Ψ₀> = ∫Ψ₀ -iħ d/dx(Ψ₀) =M

Using Integration by parts i get:

M = -Ψ₀ iħ d/dx(Ψ₀) (assuming hilbert space)

Implying the expectation values for momentum are zero , however i get all the expectation values are zero for x and momentum in both states which makes no sense :(

I don't know whether that's correct for this question, as I haven't checked; but, why do you think it makes no sense?

 

[Somali_Physicist]

I don't know whether that's correct for this question, as I haven't checked; but, why do you think it makes no sense?

Because everything being zero normally means I am wrong.

 

[Delta2]

I worked out 2.2 abit and also I got that the expectation values for position and momentum for state $\psi_0$ are zero. And I think the same hold for state $\psi_1$. It is because we always get a product of an odd and an even function in the integrals (since $\psi_0$ is even, $\psi_0'$ is odd ,$\psi_0''$ is even and x is odd). So at the very end we get integrals of an odd function which gives zero.