相关论文: Generalized Coherent States Associated with the $C…
We consider the problem of existence of the diagonal representation for operators in the space of a family of generalized coherent states associated with an unitary irreducible representation of a (compact) Lie group. We show that necessary…
The earlier treatments of Lorentz covariant harmonic oscillator have brought to light various difficulties, such as reconciling Lorentz symmetry with the full Fock space, and divergence issues with their functional representations. We…
We build the coherent states for a family of solvable singular Schr\"odinger Hamiltonians obtained through supersymmetric quantum mechanics from the truncated oscillator. The main feature of such systems is the fact that their…
Recently a $f$-deformed Fock space which is spanned by $|n>_{\lambda}$ has been introduced. These bases are indeed the eigen-states of a deformed non-Hermitian Hamiltonian. In this contribution, we will use a rather new non-orthogonal basis…
In this paper we construct manifestly covariant relativistic coherent states on the entire complex plane which reproduce others previously introduced on a given $SL(2,R)$ representation, once a change of variables $z\in C\rightarrow z_D \in…
This paper describes how the structure of the state space of the quantum harmonic oscillator can be described by an adjunction of categories, that encodes the raising and lowering operators into a commutative comonoid. The formulation is an…
The canonical coherent states are expressed as infinite series in powers of a complex number $z$ in their infinite series version. In this article we present classes of coherent states by replacing this complex number $z$ by other choices,…
Coherent states of the two dimensional harmonic oscillator are constructed as superpositions of energy and angular momentum eigenstates. It is shown that these states are Gaussian wave-packets moving along a classical trajectory, with a…
We consider a one-parameter family of nonlinear coherent states by replacing the factorial in coefficients of the canonical coherent states by a specific generalized factorial depending on a parameter gamma. These states are superposition…
We construct a new class of coherent states indexed by points z of the complex plane and depending on two positive parameters m and epsilon by replacing the coefficients of the canonical coherent states by polyanalytic functions. These…
A geometric characterization of transition amplitudes between coherent states, or equivalently, of the hermitian scalar product of holomorphic cross sections in the associated D - M tilda - module, in terms of the embedding of the cohe-…
A set of generalized squeezed-coherent states for the finite u(2) oscillator is obtained. These states are given as linear combinations of the mode eigenstates with amplitudes determined by matrix elements of exponentials in the su(2)…
We emphasize some properties of coherent state groups, i.e. groups whose quotient with the stationary groups, are manifolds which admit a holomorphic embedding in a projective Hilbert space. We determine the differential action of the…
We study the known coherent states of a quantum harmonic oscillator from the standpoint of the original developed noncommutative integration method for linear partial differential equations. The application of the method is based on the…
The relationship between states obtained by the non-commutative integration method of the Schr\"odinger equation on Lie groups and generalized coherent states is investigated. It is shown that such solutions belong to the class of…
Schr\" odinger-Robertson uncertainty relation is minimized for the quadrature components of Weyl generators of the algebra $su(N)$. This is done by determining explicit Fock-Bargamann representation of the $su(N)$ coherent states and the…
A generalization of the canonical coherent states of a quantum harmonic oscillator has been performed by requiring the conditions of normalizability, continuity in the label and resolution of the identity operator with a positive weight…
We introduce new generalized $q$-deformed coherent states ($q$-CS) by replacing the $q$-factorial of $[n]_q!$ in the series expansion of the classical $q$-CS by the generalized factorial $x_n^{q,\alpha}!$ where $x_n^{q,\alpha}=(1+\alpha…
A new oscillator-like system called by the Legendre oscillator is introduced in this note. The two families of coherent states (coherent states as eigenvectors of the annihilation operator and the Klauder-Gazeau temporally stable coherent…
States which minimize the Schr\"odinger--Robertson uncertainty relation are constructed as eigenstates of an operator which is a element of the $h(1) \oplus \su(2)$ algebra. The relations with supercoherent and supersqueezed states of the…