A momentum problem

  • #1
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(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:

Answers and Replies

  • #2
dextercioby
Science Advisor
Homework Helper
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Actually it increases with "n"...You have square root form a "n^{2}"...It looks okay...Though you didn't show the calculations leading to [itex] \Delta x [/itex]...

Daniel.
 

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