# Time propagation

1. Aug 11, 2008

### Incognition

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. Aug 11, 2008

### CompuChip

By definition
$$\exp(A) = 1 + A + \frac{1}{2} A^2 + \frac{1}{6} A^3 + \cdots$$

So exp(0) = 1
with 1 the identity matrix $$\begin{pmatrix}1&0\\0&1\end{pmatrix}$$.