# Particle in an infinite potential well, showing the uncertainty in x

1. Jun 1, 2008

I've got this question and I'm absolutely clueless, any help will be greatly appreciated:

The nth energy level for a particle of mass m confined in an infinite potential well is :

E = h^2n^2/8ml^2

where L is the width of the well and h is Planck’s constant. Assuming that the uncertainty in the particle’s momentum is equal to the momentum itself, show that the uncertainty in the particle’s position is less than the width of the well by a factor of n.

2. Jun 1, 2008

### lbrits

Figure out it's momentum. Calculate uncertainty. Use uncertainty principle. Hint: the Hamiltonian is $$\frac{p^2}{2m}$$.

3. Jun 1, 2008

Don't really know what 'hamiltonian' means but anyway I substituted in p^2/2m for E

so I get p^2/2m = h^2n^2/8ml^2

re-arranging for p I get: p = hn/2l

not entirely sure where to go from here.

4. Jun 1, 2008

### lbrits

"assuming that the uncertainty in the particle’s momentum is equal to the momentum itself"
Now use the uncertainty principle.

5. Jun 1, 2008

so delta(x) p > h-bar/2

delta(x) hn/2L > h-bar/2

delta(x) hn/2L > h/4pi

delta(x) > L/2pi(n)

...

What have I done wrong?

Last edited: Jun 1, 2008