The Unitarity of theUOperator

The $U$ operator, which connects state vectors in interaction representation for different times, can be applied meaningfully to asymptotic values of state vectors $\Phi (\pm \infty )$ if these limits exist. The conditions for this occurrence are stated for the simplest case. If the restriction resulting from the definition of the asymptotic values is respected, all $U$ operators are unambiguously unitary. A more general operator $W$ which can act on all state vectors, can be defined, but it is not unitary.