Quantum-mechanical evolution of generalized coherent states and semiclassical approximation

A. Kovner; B. Rosenstein

doi:10.1103/physrevd.32.2622

Quantum-mechanical evolution of generalized coherent states and semiclassical approximation

Physical Review D ◽

10.1103/physrevd.32.2622 ◽

1985 ◽

Vol 32 (10) ◽

pp. 2622-2626 ◽

Cited By ~ 2

Author(s):

A. Kovner ◽

B. Rosenstein

Keyword(s):

Coherent States ◽

Semiclassical Approximation ◽

Quantum Mechanical ◽

Mechanical Evolution ◽

Generalized Coherent States

Download Full-text

Groupoids and Coherent States

Open Systems & Information Dynamics ◽

10.1142/s1230161219500173 ◽

2019 ◽

Vol 26 (04) ◽

pp. 1950017 ◽

Cited By ~ 2

Author(s):

F. di Cosmo ◽

A. Ibort ◽

G. Marmo

Keyword(s):

Hilbert Space ◽

Harmonic Oscillator ◽

Coherent States ◽

Quantum Mechanical ◽

Natural Setting ◽

Invariant Subset ◽

Quantum Mechanical System ◽

Generalized Coherent States ◽

Invertible Elements ◽

Groupoid Algebra

Schwinger’s algebra of selective measurements has a natural interpretation in terms of groupoids. This approach is pushed forward in this paper to show that the theory of coherent states has a natural setting in the framework of groupoids. Thus given a quantum mechanical system with associated Hilbert space determined by a representation of a groupoid, it is shown that any invariant subset of the group of invertible elements in the groupoid algebra determines a family of generalized coherent states provided that a completeness condition is satisfied. The standard coherent states for the harmonic oscillator as well as generalized coherent states for f-oscillators are exemplified in this picture.

Download Full-text

Uncertainty Relations in the Madelung Picture

Entropy ◽

10.3390/e24010020 ◽

2021 ◽

Vol 24 (1) ◽

pp. 20

Author(s):

Moise Bonilla-Licea ◽

Dieter Schuch

Keyword(s):

Wave Function ◽

Quantum System ◽

Momentum Space ◽

Coherent States ◽

Quantum Mechanical ◽

Uncertainty Relations ◽

Hydrodynamic Equations ◽

Generalized Coherent States ◽

Complex Wave ◽

Classical Hydrodynamic

Madelung showed how the complex Schrödinger equation can be rewritten in terms of two real equations, one for the phase and one for the amplitude of the complex wave function, where both equations are not independent of each other, but coupled. Although these equations formally look like classical hydrodynamic equations, they contain all the information about the quantum system. Concerning the quantum mechanical uncertainties of position and momentum, however, this is not so obvious at first sight. We show how these uncertainties are related to the phase and amplitude of the wave function in position and momentum space and, particularly, that the contribution from the phase essentially depends on the position–momentum correlations. This will be illustrated explicitly using generalized coherent states as examples.

Download Full-text

Semi-Classical Localisation Properties of Quantum Oscillators on a Noncommutative Configuration Space

Open Systems & Information Dynamics ◽

10.1142/s1230161215500213 ◽

2015 ◽

Vol 22 (04) ◽

pp. 1550021 ◽

Cited By ~ 1

Author(s):

Fabio Benatti ◽

Laure Gouba

Keyword(s):

Phase Space ◽

Configuration Space ◽

Classical Limit ◽

Coherent States ◽

Point Of View ◽

Quantum Mechanical ◽

Wigner Functions ◽

Quantum Mechanical Oscillators ◽

Mechanical Oscillators ◽

Space Noncommutativity

When dealing with the classical limit of two quantum mechanical oscillators on a noncommutative configuration space, the limits corresponding to the removal of configuration-space noncommutativity and position-momentum noncommutativity do not commute. We address this behaviour from the point of view of the phase-space localisation properties of the Wigner functions of coherent states under the two limits.

Download Full-text