White Noise Path Integral Treatment of a Two-dimensional Dirac Oscillator in a Uniform Magnetic Field

2008 ◽  
Author(s):  
Lyndon D. Bastatas ◽  
Jinky B. Bornales ◽  
Christopher C. Bernido ◽  
M. Victoria Carpio-Bernido
Keyword(s):  
Magnetic Field ◽  
White Noise ◽  
Path Integral ◽  
Uniform Magnetic Field ◽  
Two Dimensional ◽  
Dirac Oscillator ◽  
Integral Treatment

Dirac oscillator in a uniform electric field: Path integral treatment

2019 ◽  
Vol 34 (30) ◽  
pp. 1950246
Author(s):  
Hassene Bada ◽  
Mekki Aouachria
Keyword(s):  
Energy Spectrum ◽  
Electric Field ◽  
Path Integral ◽  
Uniform Electric Field ◽  
Two Dimensional ◽  
Dirac Oscillator ◽  
Fermionic Model ◽  
Internal Motions ◽  
Integral Treatment ◽  
The One

In this paper, the propagator of a two-dimensional Dirac oscillator in the presence of a uniform electric field is derived by using the path integral technique. The fact that the globally named approach is used in this work redirects, beforehand, our search for the propagator of the Dirac equation to that of the propagator of its quadratic form. The internal motions relative to the spin are represented by two fermionic oscillators, which are described by Grassmannian variables, according to Schwinger’s fermionic model. Once the integration over the anticommuting variables (Grassmannian variables) is accomplished, the problem becomes the one of finding a non-relativistic propagator with only bosonic variables. The energy spectrum of the electron and the corresponding eigenspinors are also obtained in this work.

WHITE NOISE PATH INTEGRAL TREATMENT OF THE PROBABILITY DISTRIBUTION FOR THE AREA ENCLOSED BY A POLYMER LOOP IN CROSSED ELECTRIC-MAGNETIC FIELDS

2012 ◽  
Vol 17 ◽  
pp. 77-82
Author(s):  
BEVERLY V. GEMAO ◽  
JINKY B. BORNALES
Keyword(s):  
Magnetic Field ◽  
Brownian Motion ◽  
Probability Distribution ◽  
Magnetic Fields ◽  
White Noise ◽  
Probability Density ◽  
Path Integral ◽  
Integral Treatment ◽  
The Many ◽  
The Magnetic Field

The probability density for the area A enclosed by a polymer loop in crossed electric-magnetic fields is evaluated using the Hida-Streit formulation. In this approach, the many possible conformations of the polymer, x(v) and y(v), are represented by paths and are parametrized in terms Brownian motion. When the magnetic field is switched off, results agree with the works of Khandekar and Wiegel5

scholarly journals The exact solutions of a (2 + 1)-dimensional Dirac oscillator under a magnetic field in the presence of a minimal length

2015 ◽  
Vol 93 (5) ◽  
pp. 542-548 ◽  
Author(s):  
Abdelmalek Boumali ◽  
Hassan Hassanabadi
Keyword(s):  
Magnetic Field ◽  
Exact Solutions ◽  
Momentum Space ◽  
Uniform Magnetic Field ◽  
Hypergeometric Functions ◽  
Minimal Length ◽  
Wave Functions ◽  
Two Dimensional ◽  
Dirac Oscillator ◽  
Energy Eigenvalues

Minimal length of a two-dimensional Dirac oscillator is investigated in the presence of a uniform magnetic field and illustrates the wave functions in the momentum space. The energy eigenvalues are found and the corresponding wave functions are calculated in terms of hypergeometric functions.

Sign in / Sign up

Export Citation Format

Share Document