 Quantum symmetry of a Hamiltonian (source code)

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= Quantum symmetry of a Hamiltonian

A unitary operator $U$ is a symmetry of a time-independent Hamiltonian $H$ when
$$
U^\dagger H U=H,
$$
equivalently $[U,H]=0$. A differentiable one-parameter symmetry $U(s)=e^{-isQ/\hbar}$ has a self-adjoint generator $Q$ satisfying $[Q,H]=0$, so $Q$ is conserved.

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