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Particle in a rectangular box.

  1. Apr 2, 2007 #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: Apr 3, 2007
  2. jcsd
  3. Apr 3, 2007 #2

    cgw

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    Finally figured out the latex.
     
    Last edited: Apr 3, 2007
  4. Apr 3, 2007 #3

    Mentz114

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    Gold Member

    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".
     
  5. Apr 3, 2007 #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: Apr 3, 2007
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