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Homework Help: Spontaneous emission rates for two-level system

  1. Apr 23, 2013 #1
    1. The problem statement, all variables and given/known data

    Our quantum system has two levels:

    ψ1 = (1/[itex]\pi[/itex])1/4 * e-x2/2

    ψ2 = (4/[itex]\pi[/itex])1/4 * x * e-x2/2

    The energy of the ground state ψ1 is 0; the energy of the excited state ψ2 is [itex]\hbar[/itex] * [itex]\omega[/itex]0. What is the spontaneous emission rate for this system when it is in the excited state?

    2. Relevant equations

    I believe the equation I want to use is

    A = [itex]\frac{\omega_0^3 * |p|^2}{3*\pi*\epsilon_0*\hbar*c}[/itex],

    where the above p is drawn with a strange forward tail of sorts.

    3. The attempt at a solution

    The only equations for that strange p I can come up with is

    p = q * [itex]\sqrt{\frac{n * \hbar}{2*m*w}} * \deltan',n-1[/itex] and

    p = q * <n|x|n'>.

    The latter seems likely right, using the two given wavelengths as n and n', but then where do the energy levels come in?

    (Please excuse my Latex rustiness - I'll try to edit any lines that don't work)
    Last edited: Apr 23, 2013
  2. jcsd
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