- #1
Rahmuss
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- 0
Homework Statement
Calculate [tex]d\left\langle p\right\rangle/dt.[/tex] Answer:
Homework Equations
[tex]d\left\langle p\right\rangle/dt = \left\langle -\partial V / \partial x\right\rangle[/tex]
The Attempt at a Solution
I've been through the rigor down to getting
[tex]\left\langle -\partial V / \partial x\right\rangle + \int \hbar ^{2}/2m (\Psi ^{*} \partial ^{3}/\partial x^{3} \Psi - \partial ^{2} \Psi ^{*}/\partial x^{2} \partial \Psi /\partial x) dx[/tex]
So I have what I'm looking for (ie. [tex]d\left\langle p\right\rangle/dt = \left\langle -\partial V / \partial x\right\rangle[/tex]); but I need to prove the rest of it (what's inside the integrand) as being equal to zero. So I'm wondering if there is anything which proves that [tex]\partial ^{2}\Psi ^{*}/\partial x^{2} = \partial ^{2}\Psi /\partial x^{2}[/tex]?
If not, someone else showed me another method which uses the old [tex]d/dt (A*B) = (d/dt A *B) + (A * d/dt B)[/tex].
Any thoughts?