# Particle in a box

1. Dec 2, 2004

### Physicsiscool

Can someone please explain to me how I should go about solving the following 2 questions?

#1 The lowest energy level in a particle confined to a one-dimensional region of space with fixed dimension "L" is Eo. If an identical particle is confined to a similar region with the fixed distance (1/4)L, what is the energy of the lowest energy level that the particles have in common? Express in terms of Eo.

#2 Consider a particle in a box of width "L" and let the particle be in a state n = 11. What is the first value of x, larger then 0, where the probability of finding the particle is the highest?

2. Dec 2, 2004

### Galileo

If these are questions concerning the infinite square well, use the fact that the energy levels are:
$$E_n=n^2 \frac{\pi^2\hbar^2}{2mL^2}$$
for n=1,2,3,...

3. Dec 2, 2004

### Staff: Mentor

Write down the probability distribution for the general case with arbitrary n. (You may need to start with the wave function and find the probabilty distribution from that.) Substitute n = 11. For the particle in a box, it should be pretty obvious where the maxima are, from the general form of the probability distribution. Sketching a graph of it might help.

4. Dec 2, 2004

### Dr Transport

FOr the first part of the problem

$$E_{0} = \frac{\pi^2\hbar^2}{2mL^2}$$

for the smaller width box

$$E_{n} = 4n^{2}\frac{\pi^2\hbar^2}{2mL^2} = 4n^2 E_{0}$$

from here figure it out.