# Why do i need to define a hamiltonian to create a unitary matrix [closed]

I am reading a paper where they are defining a hamiltonian to create a unitary matrix. Why do i need a to define a hamiltonian for that and also how can i create one?

• Giving a Hermitian matrix $H$, then $e^{iH}$ is unitary. Handwavy explanation is that if $U = e^{iH}$ then $U^\dagger = \big( e^{iH} \big)^\dagger = e^{-iH}$ and therefore, $UU^\dagger = e^{iH}e^{-iH} = e^{0} = I$ which is the definition of unitary matrix. – KAJ226 Jun 3 at 17:53