Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper

    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].
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?