scholarly journals Noncommutative Phase Space Schrödinger Equation with Minimal Length

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
H. Hassanabadi ◽  
Z. Molaee ◽  
S. Zarrinkamar
Keyword(s):  
Magnetic Field ◽  
Phase Space ◽  
External Magnetic Field ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Jacobi Polynomials ◽  
Minimal Length ◽  
Two Dimensional ◽  
Noncommutative Phase Space ◽  
Energy Eigenvalues

We consider the Schrödinger equation under an external magnetic field in two-dimensional noncommutative phase space with an explicit minimal length relation. The eigenfunctions are reported in terms of the Jacobi polynomials, and the explicit form of energy eigenvalues is reported.

scholarly journals Zeeman Effect in Phase Space

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
R. A. S. Paiva ◽  
R. G. G. Amorim ◽  
S. C. Ulhoa ◽  
A. E. Santana ◽  
F. C. Khanna
Keyword(s):  
Magnetic Field ◽  
Perturbation Theory ◽  
Phase Space ◽  
External Magnetic Field ◽  
Hydrogen Atom ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Schrodinger Equation ◽  
Zeeman Effect ◽  
Two Dimensional

The two-dimensional hydrogen atom in an external magnetic field is considered in the context of phase space. Using the solution of the Schrödinger equation in phase space, the Wigner function related to the Zeeman effect is calculated. For this purpose, the Bohlin mapping is used to transform the Coulomb potential into a harmonic oscillator problem. Then, it is possible to solve the Schrödinger equation easier by using the perturbation theory. The negativity parameter for this system is realised.

scholarly journals Minimal Length Schrödinger Equation with Harmonic Potential in the Presence of a Magnetic Field

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
H. Hassanabadi ◽  
E. Maghsoodi ◽  
Akpan N. Ikot ◽  
S. Zarrinkamar
Keyword(s):  
Magnetic Field ◽  
Schrödinger Equation ◽  
Momentum Space ◽  
Schrodinger Equation ◽  
Hypergeometric Functions ◽  
Minimal Length ◽  
Wave Functions ◽  
Harmonic Potential ◽  
Energy Eigenvalues

Minimal length Schrödinger equation is investigated for harmonic potential in the presence of magnetic field and illustrates the wave functions in the momentum space. The energy eigenvalues are reported and the corresponding wave functions are calculated in terms of hypergeometric functions.

scholarly journals Two-dimensional boson oscillator under a magnetic field in the presence of a minimal length in the non-commutative space

2021 ◽  
Vol 67 (2 Mar-Apr) ◽  
pp. 226
Author(s):  
Z. Selema ◽  
A. Boumal
Keyword(s):  
Magnetic Field ◽  
Schrödinger Equation ◽  
Momentum Space ◽  
Schrodinger Equation ◽  
Minimal Length ◽  
Wave Functions ◽  
Two Dimensional ◽  
Commutative Space ◽  
Klein Gordon

Minimal length in non-commutative space of a two-dimensional Klein-Gordon oscillator isinvestigated and illustrates the wave functions in the momentum space. The eigensolutionsare found and the system is mapping to the well-known Schrodinger equation in a Pöschl-Teller potential.

Analysis of nonrelativistic particles in noncommutative phase-space under new scalar and vector interaction terms

2021 ◽  
Vol 67 (1 Jan-Feb) ◽  
pp. 84
Author(s):  
A. A. Safaei ◽  
H. Panahi ◽  
H. Hassanabadi
Keyword(s):  
Phase Space ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Wave Functions ◽  
Linear Quadratic ◽  
Noncommutative Phase Space ◽  
Energy Eigenvalues ◽  
Interaction Terms ◽  
Vector Interaction ◽  
Ansatz Approach

The Schrödinger equation in noncommutative phase space is considered with a combination of linear, quadratic, Coulomb and inverse square terms. Using the quasi exact ansatz approach, we obtain the energy eigenvalues and the corresponding wave functions. In addition, we discuss the results for various values of  in noncommutative phase space and discuss the results via various figures.

SPATIOTEMPORAL PATTERNS IN LANGMUIR PLASMAS

1994 ◽  
Vol 08 (24) ◽  
pp. 1503-1510 ◽  
Author(s):  
CANGTAO ZHOU ◽  
X.T. HE
Keyword(s):  
Phase Space ◽  
Schrödinger Equation ◽  
Spatial Patterns ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Numerical Results ◽  
Spatiotemporal Patterns ◽  
Two Dimensional ◽  
Fourier Space ◽  
Quintic Nonlinear Schrödinger Equation

The constitutions of the phase space, stochasticity, and the complicated patterns of Langmuir fields are investigated in terms of a two-dimensional cubic-quintic nonlinear Schrödinger equation. The numerical results obviously illustrate that the quintic non-linearity leads to the production of the complicated patterns. The mechanism to form these spatial patterns is also analyzed by measuring the spectrum of energy in Fourier space. It is shown that the complicated patterns are associated with the complexity of trajectory in phase space and the stochastic partition of energy in Fourier modes.

scholarly journals Thermal properties of a two-dimensional Duffin–Kemmer–Petiau oscillator under an external magnetic field in the presence of a minimal length

2020 ◽  
Vol 35 (33) ◽  
pp. 2050278
Author(s):  
H. Aounallah ◽  
B. C. Lütfüoğlu ◽  
J. Kříž
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Energy Eigenvalue ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Summation Formula ◽  
Minimal Length ◽  
Two Dimensional ◽  
Relativistic Limit ◽  
Ordinary Quantum

Generalized uncertainty principle puts forward the existence of the shortest distances and/or maximum momentum at the Planck scale for consideration. In this article, we investigate the solutions of a two-dimensional Duffin–Kemmer–Petiau (DKP) oscillator within an external magnetic field in a minimal length (ML) scale. First, we obtain the eigensolutions in ordinary quantum mechanics. Then, we examine the DKP oscillator in the presence of an ML for the spin-zero and spin-one sectors. We determine an energy eigenvalue equation in both cases with the corresponding eigenfunctions in the non-relativistic limit. We show that in the ordinary quantum mechanic limit, where the ML correction vanishes, the energy eigenvalue equations become identical with the habitual quantum mechanical ones. Finally, we employ the Euler–Mclaurin summation formula and obtain the thermodynamic functions of the DKP oscillator in the high-temperature scale.

scholarly journals (2+1)-Dimensional Duffin-Kemmer-Petiau Oscillator under a Magnetic Field in the Presence of a Minimal Length in the Noncommutative Space

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Bing-Qian Wang ◽  
Zheng-Wen Long ◽  
Chao-Yun Long ◽  
Shu-Rui Wu
Keyword(s):  
Magnetic Field ◽  
Probability Density ◽  
Momentum Space ◽  
Jacobi Polynomials ◽  
Minimal Length ◽  
Wave Functions ◽  
Noncommutative Space ◽  
Space Representation ◽  
Energy Eigenvalues ◽  
Special Cases

Using the momentum space representation, we study the (2 + 1)-dimensional Duffin-Kemmer-Petiau oscillator for spin 0 particle under a magnetic field in the presence of a minimal length in the noncommutative space. The explicit form of energy eigenvalues is found, and the wave functions and the corresponding probability density are reported in terms of the Jacobi polynomials. Additionally, we also discuss the special cases and depict the corresponding numerical results.

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