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Energy levels in quantum well structures

  1. Dec 10, 2007 #1
    Does anyone knows how to solve the following eigenvalue equation using matlab? so as to obtain the energy levels in a quantum well structure.. or does anyone has the codes or knows where to find the codes to do so?

    Eigenvalue equation:

    tan(sq_root(2mE/hbar^2)*(d/2)) = sq_root((V-E)/E) for even mode (n=2,4,6...)

    cot(sq_root(2mE/hbar^2)*(d/2)) = -sq_root((V-E)/E) for odd mode (n=1,3,5...)

    where V is the depth of the potential well and m is the effective mass. The eignvalue equation shown above can be numerically solved to yield the energy levels E in a potential well.
  2. jcsd
  3. Dec 10, 2007 #2

    George Jones

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    Staff Emeritus
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    Gold Member

    Can't you just write, e.g.,

    0 = tan(sq_root(2mE/hbar^2)*(d/2)) - sq_root((V-E)/E),

    and use the fzero command.
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