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1D Quantum Well - I'm getting something very basic wrong!

  1. May 10, 2009 #1
    Ok, so this example question is in my lecture notes:

    1. The problem statement, all variables and given/known data

    "For a 1-D quantum well, 5nm width, 2eV barrier height, calculate the number of energy levels in the well."

    2. Relevant equations

    So the equation given is a familiar one:

    [tex]E_n=\frac{n^2 \pi^2 \hbar^2}{2 m L^2}[/tex]

    and he also said [tex]E_n=2 \times 1.6 \times 10^{-19} J[/tex]

    3. The attempt at a solution

    Now, in the lecture [tex]n^2[/tex] came out to be 134, but I keep getting ~1.9, so I'm using the wrong units somewhere or something, because otherwise it's a pretty simple 'plug and chug' exercise..!

    also, I'm using
    [tex]\hbar = 6.582 \times 10^{-16} eVs[/tex]
    [tex]m = 0.511MeV[/tex]

    Can anyone help? :-s

    -Jam
     
    Last edited: May 10, 2009
  2. jcsd
  3. May 10, 2009 #2
    Remember that the units of mass are

    [tex][m] = eV/c^2[/tex]

    And therefore with the values that you are using it should be

    [tex]E_n=\frac{n^2 \pi^2 \hbar^2 c^2}{2 m L^2}[/tex]
     
  4. May 10, 2009 #3
    Hi, thanks for the reply!

    Unfortunately, if I put in the factor of [tex]c^2[/tex], then [tex]n^2[/tex] becomes ~[tex]2.13^{-17}[/tex], even further off the 134 that it should be :-(
     
  5. May 10, 2009 #4
    Make sure that you use the same units for everything. That is if you use electron volts as you said in your first post then E = 2 eV. If you use Joules for E then you have to use Js for h, kg for m (without c^2 this time) and so on.
     
  6. May 10, 2009 #5

    diazona

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    Homework Helper

    I get 133, which seems pretty close... it's probably just a silly math mistake. If you write out the details of your calculations (and please be consistent with the units ;-), someone can probably pinpoint where it went wrong.
     
  7. May 10, 2009 #6
    Ah, thankyou! Yes, it was a silly mistake, I forgot to change [tex]E=2 \times 1.6 \times 10^{-19}[/tex] to E = 2, yes it works out fine now.

    Thank you both, I have an exam tomorrow where this will likely be part of a question or two, so I'm very grateful for the help!
     
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