# Significance of the hamiltonian commuting

1. Oct 9, 2007

### sridhar

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

2. Oct 9, 2007

### nrqed

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.