- #1

- 126

- 2

[Note from mentor: this thread originated in a non-homework forum, therefore it doesn't use the standard homework template]

------------------------------------------

This exercise pops up in the Cavendish Quantum Mechanics Primer (M. Warner and A. Cheung) but I can't seem to figure it out. So far, when looking at the infinite square well of width a (and at this point in the book complex wavefunctions are not yet considered), the general form of the wave function is [itex]A_nsin(k_nx)[/itex] where [itex]k_n=\frac{\sqrt{2mE}}{\hbar}=\frac{n\pi}{a}=\frac{2\pi}{\lambda}[/itex].

I am really at a loss here. I was thinking about [itex]\langle x^2 \rangle - \langle x\rangle[/itex] but I don't know how to apply it here.

The answer should be [itex]a^2\left(\frac{1}{12}-\frac{1}{2\pi ^2n^2}\right)[/itex]...

Thanks in advance!

------------------------------------------

This exercise pops up in the Cavendish Quantum Mechanics Primer (M. Warner and A. Cheung) but I can't seem to figure it out. So far, when looking at the infinite square well of width a (and at this point in the book complex wavefunctions are not yet considered), the general form of the wave function is [itex]A_nsin(k_nx)[/itex] where [itex]k_n=\frac{\sqrt{2mE}}{\hbar}=\frac{n\pi}{a}=\frac{2\pi}{\lambda}[/itex].

I am really at a loss here. I was thinking about [itex]\langle x^2 \rangle - \langle x\rangle[/itex] but I don't know how to apply it here.

The answer should be [itex]a^2\left(\frac{1}{12}-\frac{1}{2\pi ^2n^2}\right)[/itex]...

Thanks in advance!

Last edited by a moderator: