Hi, I don't know whether the conserved quantities in QM are conserved in every conditions. For example, a state can be a non-eigenstate of energy, and when we measure the energy of this state, it falls into an eigenstate of energy. The former state does not have a definite energy, but the latter has. And, another measurment may get another different energy. Does it mean energy is not exactly conserved or it means we give the system some energy when we are measuring them? Thank you very much and happy new year!