Lowest Energy of Particle in 1-D Box: 2 eV

[Amith2006]

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)
Where does it lead to?

 

[Dick]

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

 

[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?

 

[mufusisrad]

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.

 

[Amith2006]

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]

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.

 

[Amith2006]

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