Significance of the hamiltonian commuting

[sridhar]

Wht is the significance of an operator commuting with the hamiltonian??
Its definitely more than them being measurable simultaneously and precisely!

 

[nrqed]

Wht is the significance of an operator commuting with the hamiltonian??
Its definitely more than them being measurable simultaneously and precisely!

It means that this physical quantity is conserved in time. In other words, if a state is an eigenstate fo this other operator at t=0, it will remain an eigenstate of that operator at later time. This is because the Hamiltonian is the operator that governs the time evolution of the system.