= Operator exponential
{title2=$e^A$}
For a bounded <linear operator>, the series $e^A=\sum_{n=0}^\infty A^n/n!$ converges in <operator norm>. For an unbounded <self-adjoint operator> $H$, the <spectral theorem> instead defines the bounded <unitary operator> $e^{-iHt/\hbar}$ by applying the scalar function $e^{-iEt/\hbar}$ to its <projection-valued measure>. This yields <unitary time evolution> without assuming that every vector lies in the domain of every power of $H$. In finite dimensions it is the <matrix exponential>.
Back to article page
