# Particle in a box

## Homework Statement

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?

## Homework Equations

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

## 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)

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

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?

#### Attachments

• Wave.GIF
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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.

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.

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

Dick
Homework Helper
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?

That's right. Thats cool!I think I am getting better. Thanks.