scholarly journals SEMICLASSICAL ANALYSIS OF TWO- AND THREE-SPIN ANTIFERROMAGNETS AND ANYONS ON A SPHERE

1993 ◽  
Vol 08 (19) ◽  
pp. 1805-1814 ◽  
Author(s):  
DIPTIMAN SEN
Keyword(s):  
Energy Spectrum ◽  
Spin Wave ◽  
Path Integral ◽  
Wave Functions ◽  
Total Derivative ◽  
Semiclassical Analysis

We do a semiclassical analysis for two or three spins which are coupled antiferromagnetically to each other. The semiclassical wave functions transform correctly under permutations of the spins if one takes into account the Wess-Zumino term present in the path integral for spins. The Wess-Zumino term here is a total derivative which has no effect on the energy spectrum. The semiclassical problem is related to that of anyons moving on a sphere with the statistics parameter θ being 2πS for two spins and 3πS for three spins. Finally, we present a novel way of deriving the semiclassical wave functions from the spin wave functions.

Effects of barrier penetration on energy spectrum and wave functions in the path integral formalism

1978 ◽  
Vol 136 (2) ◽  
pp. 259-276 ◽  
Author(s):  
Iring Bender ◽  
Dieter Gromes ◽  
Heinz J. Rothe ◽  
Klaus D. Rothe
Keyword(s):  
Energy Spectrum ◽  
Path Integral ◽  
Wave Functions ◽  
Integral Formalism ◽  
Path Integral Formalism ◽  
Barrier Penetration

Dirac Particle in a Constant Magnetic Field: Path Integral Treatment

2008 ◽  
Vol 63 (5-6) ◽  
pp. 283-290 ◽  
Author(s):  
Abdeldjalil Merdaci ◽  
Nadira Boudiaf ◽  
Lyazid Chetouani
Keyword(s):  
Magnetic Field ◽  
Energy Spectrum ◽  
Path Integral ◽  
Constant Magnetic Field ◽  
Dirac Particle ◽  
Wave Functions ◽  
Green Functions ◽  
Integral Treatment ◽  
Global And Local

The Green functions related to a Dirac particle in a constant magnetic field are calculated via two methods, global and local, by using the supersymmetric formalism of Fradkin and Gitman. The energy spectrum as well as the corresponding wave functions are extracted following these two approaches.

Pancharatnam phase for the generalized Jaynes–Cummings model with a nonlinear Kerr cavity

2009 ◽  
Vol 87 (4) ◽  
pp. 389-398 ◽  
Author(s):  
M. Aouachria ◽  
L. Chetouani
Keyword(s):  
Energy Spectrum ◽  
Path Integral ◽  
Population Inversion ◽  
Stark Shift ◽  
Perturbation Series ◽  
Wave Functions ◽  
Level System ◽  
Pancharatnam Phase ◽  
Atomic Population Inversion

The formalism of path integral is used to treat the influence of Stark shift on the atomic population inversion (API) and Pancharatnam phase in the Jaynes–Cummings model with a nonlinear Kerr cavity. The propagators are given explicitly as perturbation series. In the case of a quantized wave interacting with a two-level system, these are summed up exactly, and the corresponding Pancharatnam phase as well as atomic population inversion, and energy spectrum with corresponding wave functions are deduced.

Quantum Effect in the Mesoscopic Open Electron Resonator

2011 ◽  
Vol 130-134 ◽  
pp. 3259-3262
Author(s):  
Zhan Yuan Yan ◽  
Zhi Cheng Liu ◽  
Pan Zhao
Keyword(s):  
Energy Spectrum ◽  
Path Integral ◽  
Integral Method ◽  
Uncertainty Relation ◽  
Quantum Effect ◽  
Research Work ◽  
Quantum Fluctuations ◽  
Wave Functions ◽  
Path Integral Method ◽  
Open Electron

In the framework of regularization process for quantization, the mesoscopic openelectronresonator is quantized using Feynman’s path integral method. With a Gaussian type propagator, the energy spectrum and wave functions are calculated. As an application of the results, the quantum fluctuations and uncertainty relation are discussed. The detailed formulation of energy spectrum and wave functions would be benefit to the further research work of the system.

scholarly journals Path Integral Solution of PT-/non-PT-Symmetric and non-Hermitian Hulthen Potential

10.14311/1354 ◽  
2011 ◽  
Vol 51 (2) ◽  
Author(s):  
N. Kandirmaz ◽  
R. Sever
Keyword(s):  
Energy Spectrum ◽  
Path Integral ◽  
Exponential Type ◽  
Integral Solution ◽  
Wave Functions ◽  
Point Transformation ◽  
Hulthén Potential ◽  
Hulthen Potential

The wave functions and the energy spectrum of PT-/non-PT-Symmetric and non-Hermitian Hulthen potential are of an exponential type and are obtained via the path integral. The path integral is constructed using parametric time and point transformation.

Spin Wave Functions

2003 ◽  
pp. 233-252
Author(s):  
Floyd Williams
Keyword(s):  
Spin Wave ◽  
Wave Functions

Dirac particle in electric field with confining scalar potential on (anti)-de Sitter background

2018 ◽  
Vol 33 (34) ◽  
pp. 1850202 ◽  
Author(s):  
N. Messai ◽  
B. Hamil ◽  
A. Hafdallah
Keyword(s):  
Energy Spectrum ◽  
Dirac Equation ◽  
Electric Field ◽  
Scalar Potential ◽  
Dirac Particle ◽  
Wave Functions ◽  
De Sitter ◽  
Sitter Background ◽  
Position Representation

In this paper, we study the (1 + 1)-dimensional Dirac equation in the presence of electric field and scalar linear potentials on (anti)-de Sitter background. Using the position representation, the energy spectrum and the corresponding wave functions are exactly obtained.

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.

ENERGY-DEPENDENT POTENTIAL AND NORMALIZATION OF WAVE FUNCTION

2013 ◽  
Vol 28 (18) ◽  
pp. 1350079 ◽  
Author(s):  
A. BENCHIKHA ◽  
L. CHETOUANI
Keyword(s):  
Wave Function ◽  
Hydrogen Atom ◽  
Harmonic Oscillator ◽  
Path Integral ◽  
Spectral Decomposition ◽  
Wave Functions ◽  
Integral Approach ◽  
Path Integral Approach ◽  
Dependent Potential ◽  
Energy Dependent

The problem of normalization related to energy-dependent potentials is examined in the context of the path integral approach, and a justification is given. As examples, the harmonic oscillator and the hydrogen atom (radial) where, respectively the frequency and the Coulomb's constant depend on energy, are considered and their propagators determined. From their spectral decomposition, we have found that the wave functions extracted are correctly normalized.

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