Determination of time-dependent coefficients (QM)

  • Thread starter Aeon
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  • #1
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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...
 

Answers and Replies

  • #2
Bill_K
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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.
 
  • #3
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I forgot a subscript, you are right.

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

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