f-oscillators and nonlinear coherent states
TLDR
In this paper, an interpretation of the f-oscillator is provided as corresponding to a special nonlinearity of vibration for which the frequency of oscillation depends on the energy.Abstract:
The notion of f-oscillators generalizing q-oscillators is introduced. For classical and quantum cases, an interpretation of the f-oscillator is provided as corresponding to a special nonlinearity of vibration for which the frequency of oscillation depends on the energy. The f-coherent states (nonlinear coherent states) generalizing q-coherent states are constructed. Applied to quantum optics, photon distribution function, photon number means, and dispersions are calculated for the f-coherent states as well as the Wigner function and Q-function. As an example, it is shown how this nonlinearity may affect the Planck distribution formula.read more
Citations
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Journal ArticleDOI
'Nonclassical' states in quantum optics: a 'squeezed' review of the first 75 years
TL;DR: A review of studies performed in the field of non-classical states can be found in this article, with a focus on the evolution of Gaussian wave packets for an oscillator, a free particle and a particle moving in uniform constant electric and magnetic fields.
Journal ArticleDOI
Multiphoton quantum optics and quantum state engineering
TL;DR: A review of theoretical and experimental aspects of multiphoton quantum optics can be found in this paper, where the authors focus on parametric processes in nonlinear media, with special emphasis on the engineering of nonclassical states of photons and atoms that are relevant for the conceptual investigations and for the practical applications of modern quantum mechanics.
Journal ArticleDOI
Factorization: little or great algorithm?
Bogdan Mielnik,Oscar Rosas-Ortiz +1 more
TL;DR: The progress of the factorization method since the 1935 work of Dirac is briefly reviewed in this article, where the authors suggest that factorization seems an autonomous "driving force", offering substantial support to the present day Darboux and Backlund approaches.
Journal ArticleDOI
Alternative commutation relations, star products and tomography
TL;DR: In this article, the authors considered the relation between the Weyl-Wigner-Stratonovich map and the s-ordered quasi-distribution of quantum observables.
Journal ArticleDOI
Quantum states in probability representation and tomography
TL;DR: In this paper, a new formulation of quantum mechanics based on the probability representation of quantum states is given, and examples of free motion, parametric oscillator, and spin are considered.
References
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Journal ArticleDOI
On the Quantum Correction For Thermodynamic Equilibrium
TL;DR: In this article, the Boltzmann formula for the probability of a configuration is given in classical theory by means of a probability function, and the result discussed is developed for the correction term.
Book ChapterDOI
On the quantum correction for thermodynamic equilibrium
TL;DR: In this article, the Boltzmann formula for lower temperatures has been developed for a correction term, which can be developed into a power series of h. The formula is developed for this correction by means of a probability function and the result discussed.
Journal ArticleDOI
Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik
TL;DR: In der vorliegenden Arbeit werden zunachst exakte Definitionen der Worte: Ort, Geschwindigkeit, Energie usw. as mentioned in this paper.