ELLIPTIC EIGENSTATES FOR THE QUANTUM HARMONIC-OSCILLATOR

A new family of stationary coherent states for the two-dimensional har monic oscillator is presented. These states are coherent in the sense that they minimize an uncertainty relation for observables related to the orientation and the eccentricity of an ellipse. The wavefunction o f these states is particularly simple and well localized on the corres ponding classical elliptical trajectory. As the number of quanta incre ases, the localization on the classical invariant structure is more pr onounced. These coherent states give a useful tool to compare classica l and quantum mechanics and form a convenient basis to study weak pert urbations.