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Time propagation

  1. Aug 11, 2008 #1
    I'm running a simple limiting case of a simulation with the expression:

    exp(-i*H*t), where H is the hamiltonian, in this case a 2x2 matrix of zeros. Should this evaluate to 0, or to [ 1 1 ; 1 1] ?

    Right now my sim uses the latter, which I'm sure is wrong. What do you think? Thanks in advance.
     
  2. jcsd
  3. Aug 11, 2008 #2

    CompuChip

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    By definition
    [tex]\exp(A) = 1 + A + \frac{1}{2} A^2 + \frac{1}{6} A^3 + \cdots[/tex]

    So exp(0) = 1
    with 1 the identity matrix [tex]\begin{pmatrix}1&0\\0&1\end{pmatrix}[/tex].
     
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