An Elementary Construction on Nonlinear Coherent States Associated to Generalized Bargmann Spaces

Abdelkader Intissar

International Journal of Mathematics and Mathematical Sciences, 2010, vol. 2010, 1-15

Abstract:

Consider the space ð ¿ 2 ( â„‚ , ð ‘‘ 𠜇 ( 𠑧 ) ) , where ð ‘‘ 𠜇 ( 𠑧 ) = ð ‘’ − | 𠑧 | 2 â‹€ ð ‘‘ ð ‘‘ 𠑧 𠑧 is the Gaussian measure, and its generalized Bargmann subspaces ð ¸ ð ‘š which are the null kernels of the operator Δ = − 𠜕 2 / 𠜕 𠑧 𠜕 𠑧 + 𠑧 ( 𠜕 / 𠜕 𠑧 ) − ð ‘š ð ¼ ; ð ‘š = 0 , 1 , … . In this work, we present an other construction of ð ¸ ð ‘š following the Hermite functions which allows us to define a family of generalized Bargmann transform ð µ ð ‘š which maps isometrically ð ¸ ð ‘š into ð ¿ 2 ( â„ ) . The generalized coherent states ∣ 𠑧 ⟩ ð ‘š associated to ð ¸ ð ‘š are constructed and some properties of them are given.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:357050

DOI: 10.1155/2010/357050

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