Coherent states on the circle

González, José Luís Galán; Olmo, M. A. del

doi:10.1088/0305-4470/31/44/012

Cited by 82 publications

(137 citation statements)

References 10 publications

Supporting

Mentioning

133

Contrasting

Order By: Relevance

“…For the special case of G = U(1), i.e. quantum mechanics on the circle, the complexifier coherent states reduce to the already employed coherent states on the circle, which had either been derived from a generalization of the harmonic oscillator coherent states [3,5,16], or simply guessed [15,20]. In [2], one can find an extensive description of these states and their properties.…”

Section: Introductionmentioning

confidence: 99%

Quantum mechanics on a circle: Husimi phase-space distributions and semiclassical coherent state propagators

Bähr¹,

Korsch²

2007

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

We discuss some basic tools for an analysis of one-dimensional quantum systems defined on a cyclic coordinate space. The basic features of the generalized coherent states, the complexifier coherent states, are reviewed. These states are then used to define the corresponding (quasi)densities in phase space. The properties of these generalized Husimi distributions are discussed, in particular their zeros. Furthermore, the use of the complexifier coherent states for a semiclassical analysis is demonstrated by deriving a semiclassical coherent state propagator in phase space.

show abstract

Section: Introductionmentioning

confidence: 99%

Quantum mechanics on a circle: Husimi phase-space distributions and semiclassical coherent state propagators

Bähr¹,

Korsch²

2007

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…Being inspired by the choice of the coherent states for the motion of a particle on a circle [26,27,28,29,30], we define φ …”

Section: Choice Of Coherent Statesmentioning

confidence: 99%

Coherent state quantization of a particle in de Sitter space

Gazeau¹,

Piechocki²

2004

J. Phys. A: Math. Gen.

View full text Add to dashboard Cite

We present a coherent state quantization of the dynamics of a relativistic test particle on onesheet hyperboloid embedded in three-dimensional Minkowski space. The group SO 0 (1, 2) is considered to be the symmetry group of the system. Our procedure relies on the choice of coherent states of the motion on a circle. The coherent state realization of the principal series representation of SO 0 (1, 2) seems to be a new result.

show abstract

“…We also introduce an analogous formalism on a strip for quantum systems on a circle. Quantum mechanics 2 on a circle, has been studied for a long time [20][21][22][23][24][25][26][27], and coherent states on a circle have been considered in [28][29][30][31]. Our approach complements this work, using an analytic language with Theta functions.…”

Section: Introductionmentioning

confidence: 99%