Quantum mechanics on operator [closed]

If any operator is commute with Hamilton then they are labelled such a way that the energy eigenstate are equal and we also know it is a constant of motion. I don't related constant of motion with above theory. please help me

closed as unclear what you're asking by JMac, John Rennie, GiorgioP, Aaron Stevens, Jon CusterApr 3 at 19:35

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Let $$A$$ be any self-adjoint operator on a Hilbert space and $$H$$ the Hamiltonian of a quantum system: one can show (Ehrenfest theorem) that $$\frac{d}{dt}\langle A \rangle = \frac{1}{i\hbar}\langle [A, H] \rangle + \langle \frac{\partial A}{\partial t} \rangle$$ where $$\langle A \rangle$$ denotes the expectation value onto a generic state $$|\psi\rangle$$. Therefore unless the operator explicitly depends on time, it is a constant of motion as long as it commutes with the Hamiltonian.