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Graduate texts in contemporary physics

Hilbert Spaces with Reproducing Kernels and Coherent States

S. Twareque Ali, Jean-Pierre Antoine, Jean‐Pierre Gazeau

Published Jan 1, 2000• 0 citations
Publisher
DOI
10.1007/978-1-4612-1258-4_5

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This work addresses a construction of a dual pair of nonlinear coherent states (NCS) in the context of changes of bases in the underlying Hilbert space for a model pertaining to an electron-phonon model in the condensed matter physics, obeying a f -deformed Heisenberg algebra.The existence and properties of reproducing kernel in the NCS Hilbert space are studied and discussed; the probability density and its dynamics in the basis of constructed coherent states are provided.A Glauber-Sudarshan P-representation of the density matrix and relevant issues related to the reproducing kernel properties are presented.Moreover, a NCS quantization of classical phase space observables is performed and illustrated in a concrete example of q-deformed coherent states.Finally, an exposition of quantum optical properties is given.