SOLUTIONS FOR THE LANDAU PROBLEM USING SYMPLECTIC REPRESENTATIONS OF THE GALILEI GROUP-Reference-Cited by-同舟云学术

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

Published:2013-03-10 Issue:05n06 Volume:28 Page:1350013
ISSN:0217-751X
Container-title:International Journal of Modern Physics A
language:en
Short-container-title:Int. J. Mod. Phys. A

Author:

AMORIM R. G. G.¹²,FERNANDES M. C. B.²,KHANNA F. C.³⁴,SANTANA A. E.²,VIANNA J. D. M.²⁵

Affiliation:

1. Instituto Federal de Educação, Ciência e Tecnologia de Goiás, Campus de Luziânia, 72811-580, Luziânia, GO, Brazil

2. International Centre for Condensed Matter Physics, Instituto de Física, Universidade de Brasília, 70910-900, Brasília, DF, Brazil

3. Department of Physics, Theoretical Physics Institute, University of Alberta, Edmonton, Alberta, Canada T6G 2J1, Canada

4. TRIUMF, 4004, Westbrook Mall, Vancouver, British Columbia, Canada V6T 2A3, Canada

5. Instituto de Física, Universidade Federal da Bahia, 40210-340, Salvador, BA, Brazil

Abstract

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Astronomy and Astrophysics,Nuclear and High Energy Physics,Atomic and Molecular Physics, and Optics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0217751X13500139

Reference58 articles.

1. Distribution functions in physics: Fundamentals

2. Features of time-independent Wigner functions

3. DEFORMATION QUANTIZATION: QUANTUM MECHANICS LIVES AND WORKS IN PHASE-SPACE

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