Related papers: Coherent-State Overcompleteness, Path Integrals, a…
Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert…
This paper defines coherent manifolds and discusses their properties and their application in quantum mechanics. Every coherent manifold with a large group of symmetries gives rise to a Hilbert space, the completed quantum space of $Z$,…
We construct a system of coherent states for the hydrogen atom that is expressed in terms of elementary functions. Unlike to the previous attempts in this direction, this system possesses the properties equivalent to the most of those for…
The quantum metrological performance of spin coherent states superposition is considered, and conditions for measurements with the Heisenberg-limit (HL) precision are identified. It is demonstrated that the choice of the…
The three approaches to relativistic generalization of coherent states are discussed in the simplest case of a spinless particle: the standard, canonical coherent states, the Lorentzian states and the coherent states introduced by Kaiser…
We formulate the coherent state path integral on a two dimensional noncommutative plane using the fact that noncommuative quantum mechanics can be viewed as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on…
In this paper, the Higgs-like approach is used to analyze the quantum dynamics of a harmonic oscillator constrained on a circle. We obtain the Hamiltonian of this system as a function of the Cartesian coordinate of the tangent line through…
We study characteristic aspects of the geometric phase which is associated with the generalized coherent states. This is determined by special orbits in the parameter space defining the coherent state, which is obtained as a solution of the…
The quantum walk is a dynamical protocol which describes the motion of spinful particles on a lattice. Also, it has been demonstrated to be a powerful platform to explore topological quantum matter. Recently, the quantum walk in coherent…
Parallel to the quantization of the complex plane, using the canonical coherent states of a right quaternionic Hilbert space, quaternion field of quaternionic quantum mechanics is quantized. Associated upper symbols, lower symbols and…
Coherent subspaces spanned by a finite number of coherent states are introduced, in a quantum system with Hilbert space that has odd prime dimension $d$. The set of all coherent subspaces is partitioned into equivalence classes, with $d^2$…
A brief summary of the application of coherent states in the examination of quantum dynamics of cosmological models is given. We discuss quantization maps, phase space probability distributions and semiclassical phase spaces. The…
Classes of coherent states are presented by replacing the labeling parameter $z$ of Klauder-Perelomov type coherent states by confluent hypergeometric functions with specific parameters. Temporally stable coherent states for the isotonic…
A closed (in terms of classical data) expression for a transition amplitude between two generalized coherent states associated with a semisimple Lee algebra underlying the system is derived for large values of the representation highest…
Coherence, treated as a resource in quantum information theory, is a basis-dependent quantity. Looking for states that have constant coherence under canonical changes of basis yields highly symmetric structures in state space. For the case…
Coordinate atypical representation of the orthosymplectic superalgebra osp(2/2) in a Hilbert superspace of square integrable functions constructed in a special way is given. The quantum nonrelativistic free particle Hamiltonian is an…
Coherent states possess a regularized path integral and gives a natural relation between classical variables and quantum operators. Recent work by Klauder and Whiting has included extended variables, that can be thought of as gauge fields,…
The convenience of coherent state representation is discussed from the viewpoint of what is in a broad sense called the measurement problem in quantum mechanics. Standard quantum theory in coherent state representation is intrinsically…
The coherent states for the quantum particle on the circle are introduced. The Bargmann representation within the actual treatment provides the representation of the algebra $[\hat J,U]=U$, where $U$ is unitary, which is a direct…
We study numerically the coordinate wave functions and the Wigner functions of the coherent phase states (CPS), paying the main attention to their differences from the standard (Klauder--Glauber--Sudarshan) coherent states, especially in…