非谐振子Gazeau-Klauder与Klauder-Perelomov相干态

利用Kinani-Daoud方法构造了非谐振子势的Gazeau-Klauder(GK)相干态和Klauder-Perelomov(KP)相干态，表明两种相干态在非线性谐振子势下具有完全不同的形式，并对两种相干态的完备性以及各自构成的Hilbert空间进行了讨论. 对相干态的Mandel Q参数的研究表明：GK相干态服从亚Poisson统计分布，KP相干态服从超Poisson统计分布. 关键词： 非谐振子 Gazeau-Klauder相干态 Klauder-Perelomov相干态     

Gazeau-Klauder type coherent states for hypergeometric type operators

Hypergeometric type operators are shape invariant, and a factorization into a product of first order differential operators can be explicitely described in the general case. Some additional shape invariant operators depending on several parameters are defined in a natural way by starting from this general factorization. The mathematical properties of the eigenfunctions and eigenvalues of the operators thus obtained depend on the values of the parameters involved. We study the parameter dependence of orthogonality, square integrability and monotony of the eigenvalue sequence. The results obtained allow us to define certain systems of Gazeau-Klauder type coherent states and to describe some of their properties. Our systematic study recovers a number of well-known results in a natural, unified way and also leads to new findings.      

Gazeau–Klauder coherent states examined from the viewpoint of diagonal ordering operation technique

In this paper we investigate the Gazeau–Klauder coherent states using a newly introduced diagonal ordering operation technique, in order to examine some of the properties of these coherent states. The results coincide with those obtained from other purely algebraic methods, but the calculations are greatly simplified. We apply the general theory to two cases of Gazeau–Klauder coherent states: pseudoharmonic as well as the Morse oscillators.     

A theoretical scheme for generation of Gazeau-Klauder coherent states via intensity-dependent degenerate Raman interaction

A theoretical scheme is presented for generating Gazeau-Klauder coherent states (GKCSs) via the generalization of degenerate Raman interaction with coupling constant to intensity dependent coupling. Firstly, we prove that in the intensity dependent degenerate Raman interaction, under particular conditions, the modified effective Hamiltonian can be used instead of Hamiltonian in the interaction picture, for describing the atom-field interaction. We suppose that the cavity field is initially prepared in a nonlinear CS, which is not temporally stable. As we will observe, after the occurrence of the interaction between atom and field, the generated state involves a superposition of GKCSs which are temporally stable and initial nonlinear CS. Under specific conditions which may be prepared, the generated state just includes GKCS. So, in this way we produced the GKCS, successfully.     

Compact (correlated) coherent states of an electron moving in the field of a plane electromagnetic wave

Compact coherent states of the relativistic electron which satisfy the conditions of completeness and orthogonality are constructed in the field of a plane electromagnetic wave. The physical sense of the quantum parameters introduced is defined, as well as their connection with the indeterminacy of coordinates and momentum. The breakdown of the coherent state is found with respect to all possible states which correspond to various classical trajectories of a particle, and the association of the derived results with Volkov's solutions is established. Tomsk Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 45–49, February, 1993.     

Wave packet dynamics of nonlinear Gazeau–Klauder coherent states of a position-dependent mass system in a Coulomb-like potential

AD = 1 position-dependent mass approach to constructing nonlinear quantum states for a modified Coulomb potential is used to generate Gazeau–Klauder coherent states. It appears that their energy eigenvalues are scaled down by the quantum number and the nonlinearity coefficient. We study the basic properties of these states, which are found to be undefined on the whole complex plane, and some details of their revival structure are discussed.     

Correspondence between generalized binomial field states and coherent atomic states

We show that the N-photon generalized binomial states of electromagnetic field may be put in a bijective mapping with the coherent atomic states of N two-level atoms. We exploit this correspondence to simply obtain both known and new properties of the N-photon generalized binomial states. In particular, an over-complete basis of these binomial states and an orthonormal basis are obtained. Finally, the squeezing properties of generalized binomial state are analyzed.     

On the equation of state for an electron gas in an intense magnetic field

In this paper we derive the equation of state for a relativistic electron gas imbedded in a static homogeneous magnetic field of arbitrary strength. The derivation is based on the evaluation of the energy-momentum tensor and the use of Dirac's equation for such a problem. Contrary to a derivation presented several years ago, the present derivation is completely gauge-invariant. We also show how to recover, in an exact manner, the perfect gas law for the case of weak magnetic fields.     

Donor-bound electron states in a two-dimensional quantum ring under uniform magnetic field

The electron states in a two-dimensional GaAs/AlGaAs quantum ring are theoretically studied in effective mass approximation. On-centre donor impurity and uniform magnetic field perpendicular to the ring plane are taken into account. The energy spectrum with different angular momentum changes dramatically with the geometry of the ring. The donor impurity reduces the energies with an almost fixed value; however, the magnetic field alters energies in a more complex way. For example, energy levels under magnetic field will cross each other when increasing the inner radius and outer radius of the ring, leading to the fact that the arrangement of energy levels is distinct in certain geometry of the ring. Moreover, energy levels with negative angular momentum exhibit the non-monotonous dependence on the increasing magnetic field.     

On the coherent states of a free electron laser

The coherence properties of the Free Electron Laser are examined both in the single mode and multimode case.     

Bound excess electron states on subcritical size helium clusters in a magnetic field

Stable bound electron states are shown to arise on a helium cluster in an external magnetic field. They are qualitatively different from surface bound electron states and are stable for subcritical size helium clusters, for which there are no bound electron states in the absence of a magnetic field.     

Vacuum magnetic moment of an electron moving in a uniform magnetic field

The methods of quantum electrodynamics are used to study the dependence of the vacuum magnetic moment of the electron on its energy and on the magnetic field intensity. This dependence is most important in the case of strong magnetic fields. For an ultrarelativistic electron, the vacuum magnetic moment turns out to depend on the electron energy, even in a weak magnetic field.Translated from Izvestiya VUZ. Fizika, Vol. 11, No. 11, pp. 17–22, November, 1968.     

A convenient representation for describing an electron in a uniform magnetic field

The newly established single-complex-variable state vector set for the two-dimensional harmonic oscillator in Fock space is generalized to describe an electron moving in a uniform magnetic field. In this formulation, the related Feynman transformation matrix elements are easily derived.