Particle in a rectangular box.

  • Thread starter cgw
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  • #1
cgw
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I am missing something.

The question is to find the 6 lowest energy states of a particle of mass m in a box with edge lengths of [tex]L_{1}=L[/tex], [tex]L_{2}=2L[/tex], [tex]L_{3}=2L[/tex].
The answer gives [tex] E_{0}=\frac{\pi^2\hbar^2}{8mL^2}[/tex].

I would have said [tex] E_{0}=\frac{3\pi^2\hbar^2}{4mL^2}[/tex] .

What am I missing?
(the answer given for the actual question is 6, 9, 9, 12, 14, 14)
 
Last edited:

Answers and Replies

  • #2
cgw
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Finally figured out the latex.
 
Last edited:
  • #3
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Well done with the latex. Why would you say what you say ?

I don't know what you mean by "6, 9, 9, 12, 14, 14".
 
  • #4
cgw
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The question asks for the energy of the six lowest states [tex]\frac{E}{E_{0}}[/tex]. The textbook answer gives [tex] E_{0}=\frac{\pi^2\hbar^2}{8mL^2}[/tex]

The way I see it is:

E = E_0 at n1=1, n2=1, n3=1


[tex] E_{0}=\frac{\pi^2\hbar^2}{2m}\left{\left(\frac{n_{1}}{L}\right)^2+\left(\frac{n_{2}}{2L}\right)^2+\left(\frac{n_{3}}{2L}\right)^2\right}[/tex]

which should be [tex] E_{0}=\frac{3\pi^2\hbar^2}{4mL^2}[/tex]
 
Last edited:

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