Hey people, I just finished reading a chapter in a book on quantum mechanics that has deeply disturbed me. The chapter was about symmetry in quantum mechanics. It was divided in two basic parts: time dependent and time independent transformations. Time independent transformations were quite tractable in the sense that nothing special or surprising happened. The Schrödinger equation was left unchanged. For time dependent transformations a new term to the Hamiltonian had to be added in order to preserve the form of the equation. The new Hamiltonian was the same as the old one transformed plus a term involving a firs order time derivative of the transformation operator. How can that be? Aren't all inertial frames of reference equivalent? Is Schrödinger's equation not covariant? I know nothing of relativistic QM, so sorry if this question offends those who do know something about it.