Translations in quantum mechanics revisited. The point spectrum case

Abstract

We study translations in quantum mechanics for the case of a point spectrum, including translations by non-allowed amounts. We find that we obtain a copy of the original interval if we want to move to the outside of it, or to a mixture of states when moving to non-spectrum values (i.e., an interpolation eigenfunction). These results will clarify the meaning of the Pauli statement about the existence of a time operator in quantum mechanics.