Connection between Bohmian and quantum mechanics via the Wigner function

2021 ◽  
pp. 127812
Author(s):  
Moise Bonilla-Licea ◽  
Dieter Schuch
Keyword(s):  
Quantum Mechanics ◽  
Wigner Function

Phase-Space Approach to Berry Phases

2006 ◽  
Vol 13 (01) ◽  
pp. 67-74 ◽  
Author(s):  
Dariusz Chruściński
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Wigner Function ◽  
Berry Phase ◽  
Space Formulation ◽  
Berry Phases ◽  
Classical Phase Space ◽  
New Formula ◽  
Space Approach

We propose a new formula for the adiabatic Berry phase which is based on phase-space formulation of quantum mechanics. This approach sheds a new light onto the correspondence between classical and quantum adiabatic phases — both phases are related with the averaging procedure: Hannay angle with averaging over the classical torus and Berry phase with averaging over the entire classical phase space with respect to the corresponding Wigner function.

Quantum mechanics in terms of a two-parameter generalized Wigner function

1992 ◽  
Vol 166 (2) ◽  
pp. 99-106 ◽  
Author(s):  
D. Lalović ◽  
D.M. Davidović ◽  
N. Bijedić
Keyword(s):  
Quantum Mechanics ◽  
Wigner Function ◽  
Two Parameter

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

scholarly journals The Wigner function in the relativistic quantum mechanics

2016 ◽  
Vol 375 ◽  
pp. 1-15 ◽  
Author(s):  
K. Kowalski ◽  
J. Rembieliński
Keyword(s):  
Quantum Mechanics ◽  
Wigner Function ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics
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