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 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.

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.

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.

scholarly journals Некоммутативная задача Ландау о фазовом пространстве при наличии минимальной длины

2020 ◽  
pp. 188-198
Author(s):  
F.A. Dossa ◽  
J.T. Koumagnon ◽  
J.V. Hounguevou ◽  
G.Y.H. Avossevou
Keyword(s):  
Electromagnetic Field ◽  
Phase Space ◽  
Momentum Space ◽  
Hypergeometric Functions ◽  
Heisenberg Algebra ◽  
Minimal Length ◽  
Wave Functions ◽  
Energy Eigenvalues ◽  
Uvarov Method

The deformed Landau problem under a electromagnetic field is studied, where the Heisenberg algebra is constructed in detail in non-commutative phase space in the presence of a minimal length. We show that, in the presence of a minimal length, the momentum space is more practical to solve any problem of eigenvalues. From the Nikiforov-Uvarov method, the energy eigenvalues are obtained and the corresponding wave functions are expressed in terms of hypergeometric functions. The fortuitous degeneration observed in the spectrum shows that the formulation of the minimal length complements that of the non-commutative phase space. Изучается деформированная задача Ландау в электромагнитном поле, в которой алгебра Гейзенберга подробно строится в некоммутативном фазовом пространстве при наличии минимальной длины. Мы показываем, что при наличии минимальной длины импульсное пространство более практично для решения любой проблемы собственных значений. С помощью метода Никифорова-Уварова получаются собственные значения энергии, а соответствующие волновые функции выражаются через гипергеометрические функции. Случайное вырождение, наблюдаемое в спектре, показывает, что формулировка минимальной длины дополняет формулировку некоммутативного фазового пространства.

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 The bound state solutions of the D-dimensional Schrödinger equation for the Woods–Saxon potential

2016 ◽  
Vol 25 (01) ◽  
pp. 1650002 ◽  
Author(s):  
V. H. Badalov
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound State ◽  
Wave Functions ◽  
Saxon Potential ◽  
Radial Wave ◽  
Energy Eigenvalues ◽  
Quantum Numbers ◽  
Radial Schrödinger Equation ◽  
Pekeris Approximation

In this work, the analytical solutions of the [Formula: see text]-dimensional radial Schrödinger equation are studied in great detail for the Wood–Saxon potential by taking advantage of the Pekeris approximation. Within a novel improved scheme to surmount centrifugal term, the energy eigenvalues and corresponding radial wave functions are found for any angular momentum case within the context of the Nikiforov–Uvarov (NU) and Supersymmetric quantum mechanics (SUSYQM) methods. In this way, based on these methods, the same expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformed each other is demonstrated. In addition, a finite number energy spectrum depending on the depth of the potential [Formula: see text], the radial [Formula: see text] and orbital [Formula: see text] quantum numbers and parameters [Formula: see text] are defined as well.

scholarly journals Multidimensional Schrödinger Equation and Spectral Properties of Heavy-Quarkonium Mesons at Finite Temperature

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
M. Abu-Shady
Keyword(s):  
Schrödinger Equation ◽  
Quark Gluon Plasma ◽  
Plasma Diagnostics ◽  
Finite Temperature ◽  
Schrodinger Equation ◽  
Gluon Plasma ◽  
Wave Functions ◽  
Heavy Quarkonium ◽  
Energy Eigenvalues ◽  
Radial Schrödinger Equation

TheN-radial Schrödinger equation is analytically solved at finite temperature. The analytic exact iteration method (AEIM) is employed to obtain the energy eigenvalues and wave functions for all statesnandl. The application of present results to the calculation of charmonium and bottomonium masses at finite temperature is also presented. The behavior of the charmonium and bottomonium masses is in qualitative agreement with other theoretical methods. We conclude that the solution of the Schrödinger equation plays an important role at finite temperature that the analysis of the quarkonium states gives a key input to quark-gluon plasma diagnostics.

scholarly journals Solutions of Schrodinger equation and thermal properties of generalized trigonometric Poschl-Teller potential.

2020 ◽  
Vol 66 (6 Nov-Dec) ◽  
pp. 824
Author(s):  
C. O. Edet ◽  
P. O. Amadi ◽  
U. S. Okorie ◽  
A. Tas ◽  
A. N. Ikot ◽  
...  
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Hypergeometric Functions ◽  
Energy Equation ◽  
Bound State ◽  
Energy Spectra ◽  
Energy Eigenvalues ◽  
Quantum Numbers ◽  
Special Cases ◽  
Potential Parameters

Analytical solutions of the Schrödinger equation for the generalized trigonometric Pöschl–Teller potential by using an appropriate approximation to the centrifugal term within the framework of the Functional Analysis Approach have been considered. Using the energy equation obtained, the partition function was calculated and other relevant thermodynamic properties. More so, we use the concept of the superstatistics to also evaluate the thermodynamics properties of the system. It is noted that the well-known normal statistics results are recovered in the absence of the deformation parameter and this is displayed graphically for the clarity of our results. We also obtain analytic forms for the energy eigenvalues and the bound state eigenfunction solutions are obtained in terms of the hypergeometric functions. The numerical energy spectra for different values of the principal and orbital quantum numbers are obtained. To show the accuracy of our results, we discuss some special cases by adjusting some potential parameters and also compute the numerical eigenvalue of the trigonometric Pöschl–Teller potential for comparison sake. However, it was found out that our results agree excellently with the results obtained via other methods

Analytical bound-state solutions of the Schrödinger equation for the Manning–Rosen plus Hulthén potential within SUSY quantum mechanics

2018 ◽  
Vol 33 (03) ◽  
pp. 1850021 ◽  
Author(s):  
A. I. Ahmadov ◽  
Maria Naeem ◽  
M. V. Qocayeva ◽  
V. A. Tarverdiyeva
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Jacobi Polynomials ◽  
Bound State ◽  
Wave Functions ◽  
Hulthén Potential ◽  
Radial Wave ◽  
Energy Eigenvalues ◽  
Hulthen Potential

In this paper, the bound-state solution of the modified radial Schrödinger equation is obtained for the Manning–Rosen plus Hulthén potential by using new developed scheme to overcome the centrifugal part. The energy eigenvalues and corresponding radial wave functions are defined for any [Formula: see text] angular momentum case via the Nikiforov–Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. Thanks to both methods, equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is presented. The energy levels and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary [Formula: see text] states. A closed form of the normalization constant of the wave functions is also found. It is shown that, the energy eigenvalues and eigenfunctions are sensitive to [Formula: see text] radial and [Formula: see text] orbital quantum numbers.

scholarly journals Bound states of the D-dimensional Schrödinger equation for the generalized Woods–Saxon potential

2019 ◽  
Vol 34 (14) ◽  
pp. 1950107 ◽  
Author(s):  
V. H. Badalov ◽  
B. Baris ◽  
K. Uzun
Keyword(s):  
Quantum Mechanics ◽  
Energy Spectrum ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Wave Functions ◽  
Basis Set ◽  
Saxon Potential ◽  
Radial Wave ◽  
Energy Eigenvalues ◽  
Approximate Analytical Solutions

The formal framework for quantum mechanics is an infinite number of dimensional space. Hereby, in any analytical calculation of the quantum system, the energy eigenvalues and corresponding wave functions can be represented easily in a finite-dimensional basis set. In this work, the approximate analytical solutions of the hyper-radial Schrödinger equation are obtained for the generalized Wood–Saxon potential by implementing the Pekeris approximation to surmount the centrifugal term. The energy eigenvalues and corresponding hyper-radial wave functions are derived for any angular momentum case by means of state-of-the-art Nikiforov–Uvarov and supersymmetric quantum mechanics methods. Hence, the same expressions are obtained for the energy eigenvalues, and the expression of hyper-radial wave functions transforming each other is shown owing to these methods. Furthermore, a finite number energy spectrum depending on the depths of the potential well [Formula: see text] and [Formula: see text], the radial [Formula: see text] and [Formula: see text] orbital quantum numbers and parameters [Formula: see text], [Formula: see text], [Formula: see text] are also identified in detail. Next, the bound state energies and corresponding normalized hyper-radial wave functions for the neutron system of the [Formula: see text]Fe nucleus are calculated in [Formula: see text] and [Formula: see text] as well as the energy spectrum expressions of other higher dimensions are revealed by using the energy spectrum of [Formula: see text] and [Formula: see text].

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