ON ADIABATIC APPROACH TO WAVE MATRIX IN A LEE MODEL

The definition of the Möller wave matrix is discussed in a scattering problem. where the unperturbed Hamiltonian has discrete eigenvalues. It is shown rigorously for a Lee model that the wave matrix, obtained by switehing off the interaction in a suitable way at t = - ∞, gives in the limit of no switchillg a unitary wave matrix. which diagonalizes the Hamiltonian. So it is checked that the adiabatie approach is the correct one in this case. where the usual definition of the wave matrix, as lim exp [iHt] exp [- iH0t], gives no definite result. Some possible extensions of this procedure are examined together with the connection of these results with the problem of defining asymptotie states in the field theory. © 1969, Società Italiana di Fisica. All rights reserved.