- #1

- 202

- 0

**(a)**In the infinite one-dimensional well, what is [tex]p_{av}[/tex]?

**(b)**What is [tex](p^2)_{av}[/tex]?

**(c)**What is [tex]\Delta p = \sqrt{(p^2)_av - (p_av)^2}[/tex]?

**(d)**Compute [tex]\Delta p \Delta x[/tex], and compare with the Heisenberg uncertainty relationship.

Here's my working:

**(a)**[tex]p_{av}=0[/tex].

I'm not so sure about this bit

**(b)**[tex](\frac{p^2}{2m})_{av} = E_{n} = \frac{\hbar^2\pi^2n^2}{2mL^2}[/tex].

There fore [tex](p^2)_{av}=(\frac{\hbar\pi^2n^2}{L})^2[/tex]

**(c)**Therefore,

[tex]\Delta p = \frac{\hbar\pi n}{L}[/tex].

**(d)**[tex]\Delta p\Delta x = \frac{\hbar}{2}\sqrt{2n^2\pi^2 -1}[/tex]

Part (d) it seems the most suspicious, that is, the uncertainty increases with n^2. Have I done anything wrong?

Last edited: