Dynamical Symmetries of Two-Dimensional Dirac Equation with Screened Coulomb and Isotropic Harmonic Oscillator Potentials

2014 ◽  
Vol 62 (5) ◽  
pp. 663-666
Author(s):  
Qing Wang ◽  
Yu-Long Hou ◽  
Zheng-Wen Long ◽  
Jian Jing
Keyword(s):  
Dirac Equation ◽  
Harmonic Oscillator ◽  
Two Dimensional ◽  
Dynamical Symmetries ◽  
Isotropic Harmonic Oscillator

Two-dimensional isotropic harmonic oscillator approach to classical and quantum Stokes parameters

2004 ◽  
Vol 82 (10) ◽  
pp. 767-773 ◽  
Author(s):  
R D Mota ◽  
M A Xicoténcatl ◽  
V D Granados
Keyword(s):  
Harmonic Oscillator ◽  
Classical Limit ◽  
Plane Electromagnetic Wave ◽  
Stokes Parameters ◽  
Two Dimensional ◽  
Expectation Value ◽  
Isotropic Harmonic Oscillator ◽  
Pauli Matrices ◽  
Constants Of Motion ◽  
Polarization Matrix

We show that the well-known Stokes operators, defined as elements of the Jordan–Schwinger map with the Pauli matrices of two independent bosons, are equal to the constants of motion of the two-dimensional isotropic harmonic oscillator. Taking the expectation value of the Stokes operators in a two-mode coherent state, we obtain the corresponding classical Stokes parameters. We show that this classical limit of the Stokes operators, the 2 × 2 unit matrix and the Pauli matrices may be used to expand the polarization matrix. Finally, by means of the constants of motion of the classical two-dimensional isotropic harmonic oscillator, we describe the geometric properties of the polarization ellipse. Our study is restricted to the case of a monochromatic quantized-plane electromagnetic wave that propagates along the z axis.PACS Nos.: 42.50.–p, 42.25.Ja, 11.30.–j

scholarly journals On the (2 + 1)-dimensional Dirac equation in a constant magnetic field with a minimal length uncertainty

2015 ◽  
Vol 24 (02) ◽  
pp. 1550016 ◽  
Author(s):  
P. Pedram ◽  
M. Amirfakhrian ◽  
H. Shababi
Keyword(s):  
Magnetic Field ◽  
Wave Function ◽  
Dirac Equation ◽  
General Solution ◽  
Harmonic Oscillator ◽  
Constant Magnetic Field ◽  
Minimal Length ◽  
Two Dimensional ◽  
Quantum Numbers ◽  
Dirac Hamiltonian

In this paper, we exactly solve the (2 + 1)-dimensional Dirac equation in a constant magnetic field in the presence of a minimal length. Using a proper ansatz for the wave function, we transform the Dirac Hamiltonian into two two-dimensional nonrelativistic harmonic oscillator and obtain the solutions without directly solving the corresponding differential equations which are presented by Menculini et al. [Phys. Rev. D 87 (2013) 065017]. We also show that Menculini et al. solution is a subset of the general solution which is related to the even quantum numbers.

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