Main Question or Discussion Point
Consider a 3D particle in a square box. One can represent a complete set of quantum states by indexing them with their momentum component quantum numbers. So a state would be |p_x p_y p_z>. If one goes to the energy basis, two momentum states (say |1 0 0> and |0 1 0>) will correspond to the same energy. Does this mean the energy eigenstates are not a complete set due to energy degeneracies? Is there a loss if information here?