Particle in a box

  • Thread starter Amith2006
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  • #1
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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?
 

Answers and Replies

  • #2
Dick
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I don't think it leads anywhere else. Are you sure they didn't give you some other kind of information?
 
  • #3
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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

  • #4
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
427
2
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?
 
  • #6
Dick
Science Advisor
Homework Helper
26,260
619
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.
 
  • #7
427
2
:cool: Thats cool!I think I am getting better. Thanks.
 

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