Some comments on the method of complex scaling to find physical resonance states

Some basic features of the method of complex scaling are briefly reviewed. This method is associated with a similarity transformation H = UHU −1 , in which the many‐particle Hamiltonian H loses its self‐adjoint character. In connection with the eigenvalue problems for H and H, one has formally the relations ψ = Uψ and E = E. However, since the proper boundary conditions have to be satisfied, the spectrum { E } may still be subject to change: even if some eigenvalues are persistent ( E = E), others may be lost, and new eigenvalues may occur also in the complex plane. It is pointed out that these changes are related to the fact that the “dilatation operator” U is an unbounded operator, and that the eigenfunctions involved are transformed not only within the ordinary L 2 Hilbert space, but also out of and into this space. Reference to a more complete treatment is given.