# Minimum possible energy for a particle in a box

1. ### cojewmaw

1
I have a homework problem that is giving me some problems.

Consider a particle trapped in a box of size 1. All you know is that the particle is in the box. From that you can find what is called the lowest possible energy for that particle. What you really find is the energy expected for a particle whose momentum is zero but with som minimal error bar. If you say that p=0 +/- delta p, then you're really saying that the particle might as well have p=delta p. From that you can find the minimum possible energy of a particle in a box (and note that it's not 0!) (not 0 factoral, that's 1).

So I need to find the lowest possible energy. I really don't know where to start, any help would be very useful!!

2. ### Lojzek

249
You could use the formula E=p^2/2m (good for a state with clearly defined p) and replace p with dp (since this is a typical value of p, if your distribution is centered at p=0). You can get minimum value for dp from uncertainity principle. But you must know that this is only an aproximation: exact calculation involves solving Schrödinger's equation.