Évènement

Zouhair Mouayn
Faculty of Sciences and Technics (M'Ghila) Béni Mellal, Morocco
https://www.researchgate.net/profile/Zouhair_Mouayn

Date(s) : 30/01/2017   iCal
10h00 - 11h00

In general, coherent states _xX are a specific overcomplete family of normalized vectors in the Hilbert space of the problem that describes the quantum phenomena and solves the identity of as 1 = ∫ _Xdμ(x). These states have long been known for the harmonic oscillator and their properties have frequently been taken as models for defining this notion for other models. We review the definition and properties of coherent states with examples. We construct coherent states attached to Landau levels (discrete energies of a uniform magnetic field) on three known examples of Kähler manifolds X : the Poincare disk D, the Euclidean plane ℂ and the Riemann sphere Cℙ¹. After defining their corresponding integral transforms, we obtain characterization theorems for spaces of bound states of the particle. Generalization to ℂⁿ and to the complex unit ball Bⁿ and Cℙⁿ are also discussed. In these cases, we apply a coherent states quantization method to recover the corresponding Berezin transforms and we give formulae representing these transforms as functions of Laplace-Beltrami operators.

Catégories

• Séminaire