On a wavelet system associated to the eigenvectors of Q-ikP-1

The author discusses the systems of the eigenvectors of the operator Q-ikP^-1. The system constitutes an over-complete wavelet system, where the eigenvector associated with a nonreal eigenvalue is transformed to the eigenvalue associated with another nonreal eigenvalue by the affine transform. The author shows this fact in terms of the operator algebra. The eigenfunctions in position coordinate representation are simple rational functions and have a localized `wavelet-like´ shape. They satisfy the `admissibility condition´. It has been proved that in a limit the eigenvector gradually approaches a sequence of squeezed-state vectors with respect to || ||₂ as k→∞