COHERENT STATES FOR ANHARMONIC OSCILLATES HAMILTONIANS WITH EQUIDISTANT AND QUASI-EQUIDISTANT SPECTRA

Two kinds of transformation for the time-dependent Schrodinger equatio n, i.e. the differential and integral transformations, are introduced. If one considers only stationary solutions of this equation, both tra nsformations reduce to the well known Darboux transformation for the s tationary Schrodinger equation. When applied to non-stationary solutio ns, they give different results. Both transformations are invertible i n appropriate spaces. With the help of these transformations alternati ve systems of coherent states to those in the literature are obtained for isospectral Hamiltonians with equidistant spectra. These transform ations are also applied to the construction of coherent states for Ham iltonians whose spectrum consists of an equidistant part and one separ ately disposed level with an energy gap equal to the k skipped levels.