SPECTRAL-ANALYSIS OF Q-OSCILLATOR WITH GENERAL BILINEAR INTERACTION

Spectra of the most general Hermitian Hamiltonian which is bilinear in the creation and annihilation operators of a q-harmonic oscillator ar e investigated with the help of the factorization method. It is shown that there are two factorization schemes leading to discrete spectra o f complicated forms. For q-oscillator models with continuous spectrum the Hamiltonian may have normalizable eigenstates of infinite multipli city. Existence of the continuous spectrum in the interacting system i s also discussed.