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Determination of time-dependent coefficients (QM)

  1. Jan 30, 2012 #1
    Hi,

    I am trying to solve the following equation:

    [itex]\Psi(r,t) = \sum_n C_n(t) e^{-i E_n t} \psi(r)[/itex]

    to find the [itex]C_n(t)[/itex]s.

    The system I am modeling is benzene. I can, by Hückel's method, determine the time-independent solution. The apparently obvious transition from time-independent coefficients to time-dependent coefficients is troubling me. A simple plot of the squared coefficients indicates that my electron density vanishes, which is indicative of error.

    I'm wondering how is the proper way to solve for the time-dependent coefficients...
     
  2. jcsd
  3. Jan 30, 2012 #2

    Bill_K

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    Science Advisor

    Did you leave off a subscript? If you meant to write ψ(r,t) = ∑ Cn(t) exp(-iEnt) ψn(r) where the ψn(r)'s are orthonormal, then
    ∫ψ(r,t) ψn(r) dr = Cn(t) exp(-iEnt), which gives you Cn.
     
  4. Jan 30, 2012 #3
    I forgot a subscript, you are right.

    Also, the problem was that my vectors were not orthogonalized. Thanks!
     
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