1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    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


    User Avatar
    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!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook