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1. Unitarity

   Linked via "scattering matrix"

   In the canonical formulation of quantum mechanics, the time evolution of a quantum state is governed by the Hamiltonian operator ($\hat{H}$), $U(t) = e^{-i\hat{H}t/\hbar}$. For $U(t)$ to be unitary, the Hamiltonian must be Hermitian ($\hat{H} = \hat{H}^\dagger$). If the Hamiltonian were not Hermitian, the norm of the state vector, $\langle\psi(t)|\psi(t)\rangle$, would change over time, implying that probability could either be created or destroyed, violating the foundati…