scholarly journals Uncertainty Relations in the Madelung Picture

Entropy ◽  
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.

scholarly journals Groupoids and Coherent States

2019 ◽  
Vol 26 (04) ◽  
pp. 1950017 ◽  
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.

QUANTUM TREATMENT OF THREE MUTUALLY ANISOTROPIC COUPLED OSCILLATORS

2006 ◽  
Vol 20 (24) ◽  
pp. 3487-3505 ◽  
Author(s):  
M. M. NASSAR ◽  
M. SEBAWE ABDALLA
Keyword(s):  
Wave Function ◽  
Coupled Oscillators ◽  
Coherent States ◽  
Quantum Mechanical ◽  
Long Period ◽  
Quantum Mechanical Treatment ◽  
Coupling Parameters ◽  
Quantum Treatment ◽  
Schrödinger Picture ◽  
Full Quantum

A full quantum mechanical treatment of the problem of three electromagnetic fields is considered. The system consists of three different coupling parameters where the rotating and counter-rotating terms are presented. An exact solution of the wave function in the Schrödinger picture is obtained, and the connection to the coherent states wave function is given. The symmetrical ordered quasi-probability distribution function (W-Wigner function) is calculated via the wave function in the coherent states representation. The Green's function is obtained and employed to find the Bloch density matrix. The expectation value of the energy is also given. In the framework of the vacuum and even coherent states, we have discussed the phenomenon of squeezing. It has been shown that the collapse and revival phenomenon exists at ω1=ω2 and is apparent for a long period of time.

Some aspects of a weak Weyl–Heisenberg algebra deformation

2005 ◽  
Vol 83 (9) ◽  
pp. 929-939
Author(s):  
N Boucerredj ◽  
N Mebarki ◽  
A Benslama
Keyword(s):  
Wave Function ◽  
Coherent States ◽  
Deformation Parameter ◽  
Annihilation Operator ◽  
Heisenberg Algebra ◽  
Integral Approach ◽  
Displacement Operator ◽  
Fock Representation ◽  
Generalized Coherent States ◽  
Simple Formalism

In the weak deformation (WD) approximation of the Weyl–Heisenberg algebra, the corresponding generalized coherent states and displacement operator are constructed. It is shown that those states, and contrary to the non-deformed Weyl-Heisenberg algebra, are not eigenstates of the annihilation operator. Moreover, and as an alternative to the Chaïchian et al. Q-deformed path integral approach (where Q is the deformation parameter), using the Bargmann Fock representation, we propose in the WD approximation, a general simple formalism. As an application, we calculate the propagator and the wave function of the harmonic oscillator.PACS Nos.: 03.65.Fd, 31.15.Kb

Operators and meaning of wave function

2016 ◽  
pp. 4039-4042
Author(s):  
Viliam Malcher
Keyword(s):  
Wave Function ◽  
Quantum Theory ◽  
State Vector ◽  
The State ◽  
Physical Significance ◽  
Central Problem ◽  
Quantum Mechanical ◽  
Mechanical Description ◽  
Quantum Mechanical Description ◽  
Interpretation Of Quantum Theory

The interpretation problems of quantum theory are considered. In the formalism of quantum theory the possible states of a system are described by a state vector. The state vector, which will be represented as |ψ> in Dirac notation, is the most general form of the quantum mechanical description. The central problem of the interpretation of quantum theory is to explain the physical significance of the |ψ>. In this paper we have shown that one of the best way to make of interpretation of wave function is to take the wave function as an operator.

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

2015 ◽  
Vol 22 (04) ◽  
pp. 1550021 ◽  
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.

scholarly journals Generalized coherent states

2014 ◽  
Vol 82 (8) ◽  
pp. 742-748 ◽  
Author(s):  
T. G. Philbin
Keyword(s):  
Coherent States ◽  
Generalized Coherent States
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