Coherent states associated with two-dimensional elliptic and hyperbolic equations
https://doi.org/10.29235/1561-8323-2019-63-3-278-281
Abstract
In this article it is shown that by performing Levi–Chivita-type transformations in the two-dimensional Helmholtz and Klein–Fock-type equations, it is possible to determine coherent states in a standard way. Moreover, if in the case of the Helmholtz elliptic equation the Levi–Civita transformation is realized by a complex quadratic map, then in the case of the Klein–Foсk-type equation it is realized by an analogue of such a map however defined for functions of a double variable. The coordinate and momentum representations of the coherent state are found. The purpose of constructing coherent states in the described manner is a further development of the hadron model proposed in [1; 2].
Keywords
scalar particle,
Helmholtz equation,
Klein–Fock type equation,
Levi–Civita transformations,
creation (annihilation) operators,
coherent states,
partons,
coordinate (momentum) represantation
Supporting agencies: The work was sponsored by the Grant of the Belarusian Republican Foundation for Fundamental Research no. Ф16Д-003.
About the Author
Yu. A. Kurochkin
B. I. Stepanov Institute of Physics of the National Academy of Sciences of Belarus
Belarus
Belarus
Kurochkin Yurii Andreevich – D. Sc. (Physics and Mathematics), Head of the Center
68-2, Nezavisimosti Ave., 220072, Minsk, Republic of Belarus
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