https://doi.org/10.1140/epjp/s13360-025-06870-4
Regular Article
Coherent states of finite-level systems
1
Department of Physics, Tomsk State University, Lenin ave. 36, 634050, Tomsk, Russia
2
P.N. Lebedev Physical Institute, Leninskiy ave. 53, 119991, Moscow, Russia
3
Institute of Physics, University of São Paulo, Rua do Matão, 1371, 05508-090, São Paulo, Brazil
Received:
10
July
2025
Accepted:
15
September
2025
Published online:
25
September
2025
A method for constructing coherent states (CS) of finite-level systems with a given angular momentum is proposed. To this end we generalize the known spin equation (SE) to an infinite-dimensional Fock space. The equation describes a special quadratic system in the latter space. Its projections on d-dimensional subspaces represent analogs of SE for d-dimensional systems in an external electromagnetic field which describe d-dimensional systems with a given angular moment. Using a modification of the Malkin-Manko method developed in our earlier work, we construct the corresponding CS for the total quadratic system. Projections of the later CS on finite-dimensional subspaces we call angular moment CS (AMCS) of finite-level systems. The AMCS have a clear physical meaning; they obey the Schrödinger equation for a d-dimensional system with a given angular moment 
in an external electromagnetic field. Their possible exact solutions are constructed via exact solutions of the SE in 2-dimensional space. The latter solutions can be found analytically and are completely described in our earlier works. One subset of AMCS can be related to Perelomov spinning CS (PSCS). This reflects the fact that the set of possible AMCS is wider than the set of PSCS. AMCS states in a constant magnetic field are constructed.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
