# 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

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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.