GENERALIZED COHERENT STATES FOR THE SPHERICAL HARMONICS $Y_{m}^{m}(\theta,\phi)$

3 Generalized Spherical Harmonics

Generalized Squeezed States from Generalized Coherent States

Both the coherent states and also the squeezed states of the harmonic oscillator have long been understood from the three classical points of view: the 1) displacement operator, 2) annihilation(or ladder-) operator, and minimum-uncertainty methods. For general systems, there is the same understanding except for ladder-operator and displacement-operator squeezed states. After reviewing the known...

Spherical Harmonics

5 Spherical Harmonics 7 5.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 5.2 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 5.2.1 Harmonic expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 5.2.2 Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

Generalized Coherent States for Classical Orthogonal Polynomials

For the oscillator-like systems, connected with the Laguerre, Legendre and Chebyshev polynomials coherent states of Glauber-Barut-Girardello type are defined. The suggested construction can be applied to each system of orthogonal polynomials including classical ones as well as deformed ones.

Dynamics of Generalized Coherent States

We show that generalized coherent states follow Schrödinger dynamics in time-dependent potentials. The normalized wave-packets follow a classical evolution without spreading; in turn, the Schrödinger potential depends on the state through the classical trajectory. This feedback mechanism with continuous dynamical re-adjustement allows the packets to remain coherent indefinetely. PACS numbers: 0...