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Hamiltonian operator

Quantum symmetry of a Hamiltonian

If $U(s)=e^{-isQ/\hbar}$ and $U(s)^\dagger H U(s)=H$, differentiation at $s=0$ gives
$$
[Q,H]=0.
$$
In the <Heisenberg picture>,
$$
\frac{dQ}{dt}=\frac i\hbar[H,Q]=0.
$$

Conserved generator of a continuous quantum symmetry

Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 1 / 34B / a / Solution

Conserved generator of a continuous quantum symmetry

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Conserved generator of a continuous quantum symmetry

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