- #1
broegger
- 257
- 0
I am trying to prove that
[tex] \frac{d\langle p \rangle}{dt} = \langle -\frac{\partial V}{\partial x} \rangle [/tex]
I am done if I can just prove that
[tex] \left[ \Psi^*\frac{\partial^2 \Psi}{\partial x^2} \right]_{-\infty}^{\infty} = 0 [/tex]
[tex] \left[ \frac{\partial \Psi}{\partial x} \frac{\partial \Psi^*}{\partial x} \right]_{-\infty}^{\infty} = 0 [/tex]
My suggestion is that since [tex]\Psi[/tex] is a wavefunction, it is normalizable and must approach 0 as [tex]x \rightarrow \pm\infty[/tex], and so must its derivatives. I don't know if this argument holds?
[tex] \frac{d\langle p \rangle}{dt} = \langle -\frac{\partial V}{\partial x} \rangle [/tex]
I am done if I can just prove that
[tex] \left[ \Psi^*\frac{\partial^2 \Psi}{\partial x^2} \right]_{-\infty}^{\infty} = 0 [/tex]
[tex] \left[ \frac{\partial \Psi}{\partial x} \frac{\partial \Psi^*}{\partial x} \right]_{-\infty}^{\infty} = 0 [/tex]
My suggestion is that since [tex]\Psi[/tex] is a wavefunction, it is normalizable and must approach 0 as [tex]x \rightarrow \pm\infty[/tex], and so must its derivatives. I don't know if this argument holds?
Last edited: