Floquet theory in phase space quantum mechanics for an electron in a rotating magnetic field

AbstractThe charged particle confined by a harmonic potential in a noncommutative planar phase space interacting with a homogeneous dynamical magnetic field and Aharonov-Bohm potentials is studied. We find that the canonical orbital angular momenta of the reduced models, which are obtained by setting the mass and a dimensionless parameter to zero, take fractional values. These fractional angular momenta are not only determined by the flux inside the thin long solenoid but also affected by the noncommutativities of phase space.

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STAR PRODUCTS ON GENERALIZED COMPLEX MANIFOLDS

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887807002533 ◽

2007 ◽

Vol 04 (08) ◽

pp. 1231-1238

Author(s):

JOSÉ M. ISIDRO

Keyword(s):

Magnetic Field ◽

Quantum Mechanics ◽

Phase Space ◽

Complex Manifold ◽

Holomorphic Functions ◽

Star Products ◽

Smooth Functions ◽

Background Magnetic Field ◽

Generalized Complex ◽

Classical Phase Space

We regard classical phase space as a generalized complex manifold and analyze the B-transformation properties of the ⋆-product of functions. The C⋆-algebra of smooth functions transforms in the expected way, while the C⋆-algebra of holomorphic functions (when it exists) transforms nontrivially. The B-transformed ⋆-product encodes all the properties of phase-space quantum mechanics in the presence of a background magnetic field.

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Exact Solutions of the (2+1)-Dimensional Dirac Oscillator under a Magnetic Field in the Presence of a Minimal Length in the Non-commutative Phase Space

Zeitschrift für Naturforschung A ◽

10.1515/zna-2015-0140 ◽

2015 ◽

Vol 70 (8) ◽

pp. 619-627 ◽

Cited By ~ 10

Author(s):

Abdelmalek Boumali ◽

Hassan Hassanabadi

Keyword(s):

Magnetic Field ◽

Quantum Mechanics ◽

Phase Space ◽

Hypergeometric Functions ◽

Relativistic Quantum ◽

Minimal Length ◽

Wave Functions ◽

Relativistic Quantum Mechanics ◽

Two Dimensional ◽

Dirac Oscillator

AbstractWe consider a two-dimensional Dirac oscillator in the presence of a magnetic field in non-commutative phase space in the framework of relativistic quantum mechanics with minimal length. The problem in question is identified with a Poschl–Teller potential. The eigenvalues are found, and the corresponding wave functions are calculated in terms of hypergeometric functions.

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Geometric phase in quantum mechanics and calculation for spin one-half in a rotating magnetic field

Canadian Journal of Physics ◽

10.1139/p2012-063 ◽

2012 ◽

Vol 90 (7) ◽

pp. 605-609

Author(s):

Paul Bracken

Keyword(s):

Magnetic Field ◽

Quantum Mechanics ◽

Quantum System ◽

Geometric Phase ◽

Rotating Magnetic Field ◽

Mathematical Formalism ◽

Geometric Phases

A mathematical formalism for describing geometric phases is presented. A development of the geometric phase is given, which is valid for noncyclic nonadiabatic processes. The result is used to calculate exactly the geometric phase for a quantum system that is made up of a spin one-half system in a rotating magnetic field.

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