- #1
i_hate_math
- 150
- 2
In 1D QM:
I understand that if a given potential well, U(x), is symmetric about x = L, then the expectation value for operator [x] would be <x> = L. (I am not even entirely sure why this is, guessing that the region where x<L and x>L are equally probable)
Is it possible to draw conclusion about expectation values of other operators?
Heres one example:
Given ψ(x) = sin(nπx/2L) for a infinite potential well with barriers at x=0 and x=2L,
Using symmetry arguments or otherwise, explain why or show that the expectation value of the particle momentum in this infinite well is <p> = 0
I got <p> = 0 by applying the momentum operator [p]ψ and evaluated it at the point of symmetry x=L, which gave [p]ψ = 0 (at x=L). => <p> = ∫ψ*[p]ψ = 0
Is that correct? Could someone explain to me what really is the "symmetry argument"?
Cheers
I understand that if a given potential well, U(x), is symmetric about x = L, then the expectation value for operator [x] would be <x> = L. (I am not even entirely sure why this is, guessing that the region where x<L and x>L are equally probable)
Is it possible to draw conclusion about expectation values of other operators?
Heres one example:
Given ψ(x) = sin(nπx/2L) for a infinite potential well with barriers at x=0 and x=2L,
Using symmetry arguments or otherwise, explain why or show that the expectation value of the particle momentum in this infinite well is <p> = 0
I got <p> = 0 by applying the momentum operator [p]ψ and evaluated it at the point of symmetry x=L, which gave [p]ψ = 0 (at x=L). => <p> = ∫ψ*[p]ψ = 0
Is that correct? Could someone explain to me what really is the "symmetry argument"?
Cheers