The energy level structure of the q deformed harmonic oscillator in a finite dimensional Hilbert space is studied.The Coherent states of the q deformed harmonic oscillator in a finite dimensional Hilbert space are constructed.It is shown that the energy level structure and the dynamic action are very different from that of usual harmonic oscillator due to the finiteness of the dimension of Hilbert space and the deformation parameter′s influence,and the coherent states are different from the Glauber coherent states.The energy level structure of the q deformed harmonic oscillator in a finite dimensional Hilbert space is studied.The Coherent states of the q deformed harmonic oscillator in a finite dimensional Hilbert space are constructed.It is shown that the energy level structure and the dynamic action are very different from that of usual harmonic oscillator due to the finiteness of the dimension of Hilbert space and the deformation parameter′s influence,and the coherent states are different from the Glauber coherent states.

Acta Scientiarum Naturalium Universitatis NeimongolJan 1, 20010 citations

Coherent States and Their Applications

Jean-Pierre Antoine, Bagarello, Fabio, Jean‐Pierre Gazeau

Springer proceedings in physicsJan 1, 201835 citations

Construction of the Jaynes-Cummings interaction over the finite two-dimensional oscillator

Alejandro R. Urzúa

The interaction between a two-level atom and the finite two-dimensional oscillator in the Cartesian coordinate system is addressed. The construction of the coupling between the degenerate energy states of the finite oscillator and the two levels of the atom allows the identification of an excitation-conserved eigenbasis. A dynamical approach to the evolution of mean values of the fields mediated by the atom is shown in the interaction picture. As an example, the eigenenergies states and $\mathfrak{su}(2)$ coherent states are studied. Perspectives and prospectives are given to settle a path in the study of atomic systems coupled to finite versions of the harmonic oscillator.The interaction between a two-level atom and the finite two-dimensional oscillator in the Cartesian coordinate system is addressed. The construction of the coupling between the degenerate energy states of the finite oscillator and the two levels of the atom allows the identification of an excitation-conserved eigenbasis. A dynamical approach to the evolution of mean values of the fields mediated by the atom is shown in the interaction picture. As an example, the eigenenergies states and $\mathfrak{su}(2)$ coherent states are studied. Perspectives and prospectives are given to settle a path in the study of atomic systems coupled to finite versions of the harmonic oscillator.

arXiv:2509.07215Sep 8, 20250 citations

Generalized coherent states

A. D. Jannussis, G. Karayannis, Παναγιώτης Παναγόπουλος +1 more

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimentoOct 1, 19834 citations

Quantum phases of a three-level matter-radiation interaction model using SU(3) coherent states with different cooperation numbers

Luis Fernando Quezada, Eduardo Nahmad-Achar

We use coherent states as trial states for a variational approach to study a system of a finite number of three-level atoms interacting in a dipolar approximation with a one-mode electromagnetic field. The atoms are treated as semidistinguishable using different cooperation numbers and representations of SU(3). We focus our analysis on the quantum phases of the system as well as the behavior of the most relevant observables near the phase transitions. The results are computed for all three possible configurations ($\mathrm{\ensuremath{\Xi}}, \mathrm{\ensuremath{\Lambda}}$, and $V$ ) of the three-level atoms.We use coherent states as trial states for a variational approach to study a system of a finite number of three-level atoms interacting in a dipolar approximation with a one-mode electromagnetic field. The atoms are treated as semidistinguishable using different cooperation numbers and representations of SU(3). We focus our analysis on the quantum phases of the system as well as the behavior of the most relevant observables near the phase transitions. The results are computed for all three possible configurations ($\mathrm{\ensuremath{\Xi}}, \mathrm{\ensuremath{\Lambda}}$, and $V$) of the three-level atoms.

arXiv:1803.03129Physical Review AJun 11, 20185 citations

Generalized Coherent States

Thalanayar S. Santhanam

Springer eBooksJan 1, 19802 citations

\mathfrak{su}(2)

coherent states are studied. Perspectives and prospectives are given to settle a path in the study of atomic systems coupled to finite versions of the harmonic oscillator.

V

) of the three-level atoms.