The temporal development of the state vectors in the interaction representation is investigated for a quantum-mechanical system that has bound states. It is shown that there is a non-unitary operator which determines the variation of the state vectors of the free states. This operator satisfies the same differential equation and initial condition as the unitary operator which transforms a state vector at the remote past to the state vector at a finite time or in the remote future. The present investigation is relevant to a remark made by H. S. Snyder.

No iteration process is made use of in the general investigation. Born's method of successive approximations is discussed at the end.

• Received 7 April 1952

DOI:https://doi.org/10.1103/PhysRev.87.652