The Hamiltonian H is known as the generator of time evolution, since it defines a unitary time-evolution operator U ( t ) = e − − i H t / ℏ ℏ for each value of t . From this relation between U ( t ) and H , it follows that any observable A that commutes with H will be conserved : its expectation value will not change over time. This statement generalizes, as mathematically, any Hermitian operator A can generate a family of unitary operators parameterized by a variable t . Under the evolution generated by A , any observable B that commutes with A will be conserved. Moreover, if B is conserved by evolution under A , then A is conserved under the evolution generated by B . This implies a quantum version of the result proven by Emmy Noether in classical (Lagrangian) mechanics: for every differentiable symmetry of a Hamiltonian, there exists a corresponding conservation law.