How to Evaluate the Heisenberg Uncertainty Product for a Particle in a Box?

[zak8000]

Homework Statement

Evaluate the Heisenberg Uncertainty product (delta)p*(delta)x for any eigenstate of a particle confined to a box of width L
hints:
a] what do you expect <x> to be? justify this
b] what do you expect <p> to be? justify this
c] how is p^2 related to KE and to E for the particle?

im not really sure how to approach this question but am i correct if a take the wave function of a particle in well of length L and find its expected value of <x> and <p> and then take there product and compare it with the hysenburg uncertainty??

 

[nickjer]

$\Delta x$ is not the same thing as $\langle x\rangle$. So you can't just take the product of the two expectation values. In fact the definition of the uncertainty of a value is:

$$\Delta x = \sqrt{\langle x^2 \rangle - \langle x\rangle^2}$$