# Homework Help: Particle in a box

1. Mar 27, 2007

### Amith2006

1. The problem statement, all variables and given/known data
1) A particle inside a one dimensional box with impenetratable walls at x=-a and x=+a has an energy eigenvalue of 2 eV. What is the lowest energy that the particle can have?

2. Relevant equations
E(n) = (n^2)E(o)
where E(o)=h^2/(8mL^2)

3. The attempt at a solution

I started in the following way:
If E(o) is the zero point energy. Then,
2 eV = (n^2)E(o)

2. Mar 27, 2007

### Dick

I don't think it leads anywhere else. Are you sure they didn't give you some other kind of information?

3. Mar 28, 2007

### Amith2006

I forgot to include the wave function of the particle. When u asked whether any other information was given, I struck a way to solve this problem.
I solved it in the following way:
Let w denote the wave function of the particle.
w(n)= [n^2]E(o)
From the wave function of the particle it is clear that n=2
w(2)=2 eV = [2^2]E(o)
i.e. E(o) = 0.5 eV
Is it right?

#### Attached Files:

• ###### Wave.GIF
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4. Mar 28, 2007

The problem is still ill-determined pending knowledge of either the mass and length of the box, or the quantum number (n) describing the 2eV eigenstate. Perhaps you are given a picture of the wavefunction for the 2eV eigenstate? If so, you can count zeros to determine the quantum number, otherwise, there isn't enough information to answer the problem.

5. Mar 28, 2007

### Amith2006

Did u see the diagram? Isn't that enough to solve the problem?

6. Mar 28, 2007

### Dick

That's right.

7. Mar 28, 2007

### Amith2006

Thats cool!I think I am getting better. Thanks.