Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/14400
Title: Method of Hydrodynamic Images and Quantum Calculus in Fock-Bargmann Representation of Quantum States
Authors: Pashaev,O.K.
Keywords: Coherent states
Fock-Bargmann representation
Quantum calculus
Vortex images
Publisher: Springer
Series/Report no.: Springer Proceedings in Mathematics and Statistics
Abstract: We propose a new approach to quantum states in Fock space in terms of classical hydrodynamics. By conformal mapping of complex analytic function, representing the wave function of quantum states in Fock-Bargmann representation, we define the complex potential, describing these quantum states by incompressible and irrotational classical hydrodynamic flow. In our approach, zeros of the wave function appear as a set of point vortices (sources) in plane with the same strength, allowing interpretation of them as images in a bounded domain. For the cat states we find fluid representation as descriptive of a point source in the oblique strip domain, with infinite number of periodically distributed images. For the annular domain, the infinite set of images is described by Jackson q-exponential functions. We show that these functions represent the wave functions of quantum coherent states of the q-deformed quantum oscillator in q-Fock-Bargmann representation and describe the infinite set of point vortices, distributed in geometric progression. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.
URI: https://doi.org/10.1007/978-3-031-49218-1_5
ISBN: 978-303149217-4
ISSN: 2194-1009
Appears in Collections:Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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