Extended harmonic analysis of phase space representations for the Galilei group

1986 ◽  
Vol 6 (1) ◽  
pp. 19-45 ◽  
Author(s):  
S. Twareque Ali ◽  
Eduard Prugovečki
Keyword(s):  
Phase Space ◽  
Harmonic Analysis ◽  
Galilei Group

scholarly journals About the non-standard viewpoint on the dynamics of closed vortex filament

2018 ◽  
Vol 32 (33) ◽  
pp. 1850410 ◽  
Author(s):  
S. V. Talalov
Keyword(s):  
Phase Space ◽  
Effective Mass ◽  
Explicit Formula ◽  
Vortex Filament ◽  
Hamiltonian Description ◽  
Suggested Approach ◽  
Galilei Group ◽  
Filament Dynamics

In this paper, we construct the Hamiltonian description of the closed vortex filament dynamics in terms of non-standard variables, phase space and constraints. The suggested approach makes obvious interpretation of the considered system as a structured particle that possesses certain external and internal degrees of the freedom. The constructed theory is invariant under the transformation of Galilei group. The appearance of this group allows for a new viewpoint on the energy of a closed vortex filament with zero thickness. The explicit formula for the effective mass of the structured particle “closed vortex filament” is suggested.

Quantum harmonic analysis on phase space

1984 ◽  
Vol 25 (5) ◽  
pp. 1404-1411 ◽  
Author(s):  
R. Werner
Keyword(s):  
Phase Space ◽  
Harmonic Analysis

QUANTUM MECHANICAL GALILEI GROUP AND Q-PLANES

1992 ◽  
Vol 07 (34) ◽  
pp. 3169-3177 ◽  
Author(s):  
A.E.F. DJEMAI
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Quantum Mechanical ◽  
Galilei Group

In this work, we show that for a particular choice of translations in the phase space in the context of quantum mechanics, we get a Manin plane. In this framework, we construct the quantum mechanical Galilei group.

scholarly journals Harmonic Analysis in Phase Space and Finite Weyl–Heisenberg Ensembles

2019 ◽  
Vol 174 (5) ◽  
pp. 1104-1136 ◽  
Author(s):  
Luís Daniel Abreu ◽  
Karlheinz Gröchenig ◽  
José Luis Romero
Keyword(s):  
Phase Space ◽  
Harmonic Analysis

SOLUTIONS FOR THE LANDAU PROBLEM USING SYMPLECTIC REPRESENTATIONS OF THE GALILEI GROUP

2013 ◽  
Vol 28 (05n06) ◽  
pp. 1350013 ◽  
Author(s):  
R. G. G. AMORIM ◽  
M. C. B. FERNANDES ◽  
F. C. KHANNA ◽  
A. E. SANTANA ◽  
J. D. M. VIANNA
Keyword(s):  
Quantum Mechanics ◽  
Group Theory ◽  
Phase Space ◽  
Wigner Function ◽  
Physical Theory ◽  
Star Product ◽  
Unitary Representations ◽  
Theory Approach ◽  
Galilei Group ◽  
Symplectic Representations

Symplectic unitary representations for the Galilei group are studied. The formalism is based on the noncommutative structure of the star-product, and using group theory approach as a guide, a consistent physical theory in phase space is constructed. The state of a quantum mechanics system is described by a quasi-probability amplitude that is in association with the Wigner function. As a result, the Schrödinger and Pauli–Schrödinger equations are derived in phase space. As an application, the Landau problem in phase space is studied. This shows how this method of quantum mechanics in phase space is to be brought to the realm of spatial noncommutative theories.

scholarly journals Quantum Physics in Phase Space: an Analysis of Simple Pendulum

2018 ◽  
Vol 1 (2) ◽  
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Schrödinger Equation ◽  
Wigner Function ◽  
Schrodinger Equation ◽  
Quantum Physics ◽  
Symplectic Structure ◽  
Unitary Representations ◽  
Galilei Group ◽  
Simple Pendulum

In this work we present a brief review about quantum mechanics in phase space. The approach discussed is based in the notion of symplectic structure and star-operators. In this sense, unitary representations for the Galilei group are construct, and the Schrodinger equation in phase space is derived. The connection between phase space amplitudes and Wigner function is presented. As a new result we solved the Schrodinger equation in phase space for simple pendulum. PACS Numbers: 11.10.Nx, 11.30.Cp, 05.20.Dd

Analytical solution for quantum quartic oscillator in phase space

2020 ◽  
Vol 35 (20) ◽  
pp. 2050100
Author(s):  
A. X. Martins ◽  
T. M. R. Filho ◽  
R. G. G. Amorim ◽  
R. A. S. Paiva ◽  
G. Petronilo ◽  
...  
Keyword(s):  
Phase Space ◽  
Analytical Solution ◽  
Schrödinger Equation ◽  
Wigner Function ◽  
Schrodinger Equation ◽  
Unitary Representations ◽  
Algebraic Methods ◽  
Quantum Oscillator ◽  
Galilei Group ◽  
Lie Methods

In this work, we address the quartic quantum oscillator in phase space using two approaches: computational and algebraic methods. In order to achieve such an aim, we built simplistic unitary representations for Galilei group, as a consequence the Schrödinger equation is derived in the phase space. In this context, the amplitudes of quasi-probability are associated with the Wigner function. In a computational way, we apply the techniques of Lie methods. As a result, we determine the solution of the quantum oscillator in the phase space and calculate the corresponding Wigner function. We also calculated the negativity parameter of the analyzed system.

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