# Find minimum energy of a particle using the uncertainty principle should be easy?

1. Sep 17, 2008

### darussiaman

1. The problem statement, all variables and given/known data

A particle of mass m is confined to a one-dimensional region of length a.
a.) use the uncertainty principle to obtain an expression for the minimum energy of the particle

b.) calculate the value of this energy for a 1g bead on a 10 cm wire, and for an electron in a region of 1 A in length.

2. Relevant equations

umm, as far as I'm aware, the only thing we're supposed to know is deltax*deltap => h-bar/2 and the energy-time analog of that. This is first of 3 semesters of quantum so we're not doing anything deep here, the needed equations on all the hw problems have so far been just the basic, simple ones so this shouldn't be any different...

3. The attempt at a solution

Well, I'm not sure how to set it up. This looks like it should be an easy question but having trouble for some reason. First, is this problem saying that deltax (uncertainty in position) is equal to a? If so, then the uncertainty in momentum is deltap => h-bar/(2a). OKay, so what? Energy ... well, kinetic energy = (1/2)*momentum*velocity ... so i could multiply both sides by that and would end up with uncertainty in energy on the left side, but velocity could be anything?? The delta_energy*delta time doesn't seem to be helpful either because what is change in time?

2. Sep 17, 2008

### entorm

Re: find minimum energy of a particle using the uncertainty principle... should be ea

Energy is momentum squared divided by twice the mass:

E=p^2/2m