Effect of the Wigner–Dunkl algebra on the Dirac equation and Dirac harmonic oscillator

2018 ◽  
Vol 33 (25) ◽  
pp. 1850146 ◽  
Author(s):  
S. Sargolzaeipor ◽  
H. Hassanabadi ◽  
W. S. Chung
Keyword(s):  
Functional Analysis ◽  
Wave Function ◽  
Dirac Equation ◽  
Harmonic Oscillator ◽  
Limit State ◽  
Energy Eigenvalue ◽  
Eigenvalue Equation ◽  
Reflection Symmetry ◽  
Analysis Method ◽  
One Dimensional

In this work, we study the Dirac equation and Dirac harmonic oscillator in one-dimensional via the Dunkl algebra. By using Dunkl derivative, we solve the momentum operator and Hamiltonian that include the reflection symmetry. Based on the concept of the Wigner–Dunkl algebra and the functional analysis method, we have obtained the energy eigenvalue equation and the corresponding wave function for Dirac harmonic oscillator and Dirac equation, respectively. It is shown all results in the limit state satisfied what we had expected before.

Parity inversion property of the double ring-shaped oscillator in cylindrical coordinates

2015 ◽  
Vol 30 (39) ◽  
pp. 1550200 ◽  
Author(s):  
Dong-Sheng Sun ◽  
Fa-Lin Lu ◽  
Yuan You ◽  
Chang-Yuan Chen ◽  
Shi-Hai Dong
Keyword(s):  
Functional Analysis ◽  
Singular Point ◽  
Harmonic Oscillator ◽  
Two Dimensional ◽  
Spherical Coordinates ◽  
Analysis Method ◽  
Cylindrical Coordinates ◽  
One Dimensional ◽  
Double Ring ◽  
The One

Using the functional analysis method, we present the exact solutions of the double ring-shaped oscillator (DRSO) potential with certain parity in the cylindrical coordinates. Such a quantum system is separated to two differential equations, i.e. a one-dimensional harmonic oscillator plus an inverse square term and a two-dimensional harmonic oscillator plus an inverse square term. The key point is how to find the adapted symmetrical solutions of the one-dimensional harmonic oscillator plus an inverse square term at the singular point [Formula: see text]. The obtained results are compared with those in the spherical coordinates. We also explore intimate connections [Formula: see text] and [Formula: see text] by substituting [Formula: see text] and [Formula: see text].

scholarly journals Energy and Wave function Analysis on Harmonic Oscillator Under Simultaneous Non-Hermitian Transformations of Co-ordinate and Momentum: Iso-spectral case

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 492-497
Author(s):  
Biswanath Rath ◽  
P. Mallick
Keyword(s):  
Wave Function ◽  
Perturbation Theory ◽  
Harmonic Oscillator ◽  
Function Analysis ◽  
Energy Eigenvalue ◽  
Algebraic Approach ◽  
Wave Function Analysis ◽  
Wavefunction Analysis

AbstractWe present a complete energy and wavefunction analysis of a Harmonic oscillator with simultaneous non-hermitian transformations of co-ordinate $(x \rightarrow \frac{(x + i\lambda p)}{\sqrt{(1+\beta \lambda)}})$ and momentum $(p \rightarrow \frac {(p+i\beta x)}{\sqrt{(1+\beta \lambda)}})$ using perturbation theory under iso-spectral conditions. We observe that two different frequencies of oscillation (w1, w2)correspond to the same energy eigenvalue, - which can also be verified using a Lie algebraic approach.

scholarly journals On the Thermodynamic Properties of the Spinless Duffin-Kemmer-Petiau Oscillator in Noncommutative Plane

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Zhi Wang ◽  
Zheng-Wen Long ◽  
Chao-Yun Long ◽  
Wei Zhang
Keyword(s):  
Functional Analysis ◽  
Energy Spectrum ◽  
Thermodynamic Properties ◽  
Thermodynamic Functions ◽  
Energy Eigenvalue ◽  
Noncommutative Space ◽  
Analysis Method ◽  
Physical Systems ◽  
Noncommutative Plane ◽  
Noncommutative Parameter

The Duffin-Kemmer-Petiau oscillator for spin 0 particle in noncommutative plane is analyzed and the energy eigenvalue of the system is obtained by employing the functional analysis method. Furthermore, the thermodynamic properties of the noncommutative DKP oscillator are investigated via numerical method and the influence of noncommutative space on thermodynamic functions is also discussed. We show that the energy spectrum and corresponding thermodynamic functions of the considered physical systems depend explicitly on the noncommutative parameterθwhich characterizes the noncommutativity of the space.

scholarly journals PHENOMENOLOGICAL RELATIVISTIC STUDY OF THE ENERGY OF Α Λ IN ITS GROUND AND EXCITED STATES IN HYPERNUCLEI

2020 ◽  
Vol 2 ◽  
pp. 389
Author(s):  
G. J. Papadopoulos ◽  
C. G. Koutroulos ◽  
M. E. Grypeos
Keyword(s):  
Binding Energy ◽  
Dirac Equation ◽  
Excited States ◽  
Energy Eigenvalue ◽  
Bound State ◽  
Eigenvalue Equation ◽  
Repulsive Potentials

The binding energy B_Λ of a Λ-particle in hypernuclei is studied by means of the Dirac equation containing attractive and repulsive potentials of orthogonal shapes. The energy eigenvalue equation in this case is obtained analytically for every bound state. An attempt is also made to investigate the possibility of deriving in particular cases approximate ana­lytic expressions for B_Λ.

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.

PHENOMENOLOGICAL RELATIVISTIC STUDY OF THE ENERGY OF A Λ IN ITS GROUND AND EXCITED STATES IN HYPERNUCLEI

1994 ◽  
Vol 03 (03) ◽  
pp. 939-951
Author(s):  
G.J. PAPADOPOULOS ◽  
C.G. KOUTROULOS ◽  
M.E. GRYPEOS
Keyword(s):  
Wave Function ◽  
Binding Energy ◽  
Dirac Equation ◽  
Least Squares ◽  
Excited States ◽  
Energy Eigenvalue ◽  
Bound State ◽  
Small Component ◽  
Repulsive Potentials ◽  
Analytic Expressions

The binding energy BΛ of a Λ-particle in hypernuclei is studied by means of the Dirac equation with attractive and repulsive potentials of rectangular shapes and of the same radius. The energy eigenvalue equation in this case is obtained analytically for every bound state, as well as the large and small component of the wave function (for given BΛ). A first attempt is also made to investigate the possibility of deriving in particular cases approximate analytic expressions of BΛ for the excited states. Using various least squares fittings, numerical results for the binding energy of the Λ are given and comparisons and comments are also made.

scholarly journals An Efficient Time-Variant Reliability Analysis Method with Mixed Uncertainties

Algorithms ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 229
Author(s):  
Fangyi Li ◽  
Yufei Yan ◽  
Jianhua Rong ◽  
Houyao Zhu
Keyword(s):  
Reliability Analysis ◽  
Limit State ◽  
Random Variables ◽  
Equivalent Model ◽  
Independent Random Variables ◽  
Problem Analysis ◽  
Analysis Method ◽  
Calculation Algorithm ◽  
Reliability Problem ◽  
Interval Variables

In practical engineering, due to the lack of information, it is impossible to accurately determine the distribution of all variables. Therefore, time-variant reliability problems with both random and interval variables may be encountered. However, this kind of problem usually involves a complex multilevel nested optimization problem, which leads to a substantial computational burden, and it is difficult to meet the requirements of complex engineering problem analysis. This study proposes a decoupling strategy to efficiently analyze the time-variant reliability based on the mixed uncertainty model. The interval variables are treated with independent random variables that are uniformly distributed in their respective intervals. Then the time-variant reliability-equivalent model, containing only random variables, is established, to avoid multi-layer nesting optimization. The stochastic process is first discretized to obtain several static limit state functions at different times. The time-variant reliability problem is changed into the conventional time-invariant system reliability problem. First order reliability analysis method (FORM) is used to analyze the reliability of each time. Thus, an efficient and robust convergence hybrid time-variant reliability calculation algorithm is proposed based on the equivalent model. Finally, numerical examples shows the effectiveness of the proposed method.

scholarly journals High-order compact LOD methods for solving high-dimensional advection equations

2021 ◽  
Vol 40 (3) ◽  
Author(s):  
Bo Hou ◽  
Yongbin Ge
Keyword(s):  
Truncation Error ◽  
Three Dimensional ◽  
Taylor Series Expansion ◽  
High Order ◽  
High Dimensional ◽  
Analysis Method ◽  
Order Accuracy ◽  
Von Neumann ◽  
One Dimensional ◽  
Von Neumann Analysis

AbstractIn this paper, by using the local one-dimensional (LOD) method, Taylor series expansion and correction for the third derivatives in the truncation error remainder, two high-order compact LOD schemes are established for solving the two- and three- dimensional advection equations, respectively. They have the fourth-order accuracy in both time and space. By the von Neumann analysis method, it shows that the two schemes are unconditionally stable. Besides, the consistency and convergence of them are also proved. Finally, numerical experiments are given to confirm the accuracy and efficiency of the present schemes.

scholarly journals Exact Solutions of a Spatially Dependent Mass Dirac Equation for Coulomb Field plus Tensor Interaction via Laplace Transformation Method

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
M. Eshghi ◽  
M. Hamzavi ◽  
S. M. Ikhdair
Keyword(s):  
Dirac Equation ◽  
Laplace Transformation ◽  
Bound States ◽  
Energy Eigenvalue ◽  
Coulomb Field ◽  
Transformation Method ◽  
Arbitrary Spin ◽  
Tensor Interaction ◽  
Dependent Mass ◽  
Laplace Transformation Method

The spatially dependent mass Dirac equation is solved exactly for attractive scalar and repulsive vector Coulomb potentials including a tensor interaction potential under the spin and pseudospin (p-spin) symmetric limits by using the Laplace transformation method (LTM). Closed forms of the energy eigenvalue equation and wave functions are obtained for arbitrary spin-orbit quantum number κ. Some numerical results are given too. The effect of the tensor interaction on the bound states is presented. It is shown that the tensor interaction removes the degeneracy between two states in the spin doublets. We also investigate the effects of the spatially-dependent mass on the bound states under the conditions of the spin symmetric limit and in the absence of tensor interaction (T=0).

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