scholarly journals Exact Noncommutative Two-Dimensional Hydrogen Atom

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
B. C. Wang ◽  
E. C. Brenag ◽  
R. G. G. Amorim ◽  
V. C. Rispoli ◽  
S. C. Ulhoa
Keyword(s):  
Experimental Data ◽  
Hydrogen Atom ◽  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Two Dimensional ◽  
Exact Analysis

In this work, we present an exact analysis of the two-dimensional noncommutative hydrogen atom. In this study, the Levi-Civita transformation was used to perform the solution of the noncommutative Schrodinger equation for Coulomb potential. As an important result, we determine the energy levels for the considered system. Using the result obtained and experimental data, a bound on the noncommutativity parameter was obtained.

ARBITRARY l-WAVE SOLUTIONS OF THE SCHRÖDINGER EQUATION FOR THE SCREEN COULOMB POTENTIAL

2013 ◽  
Vol 22 (06) ◽  
pp. 1350036 ◽  
Author(s):  
SHISHAN DONG ◽  
GUO-HUA SUN ◽  
SHI-HAI DONG
Keyword(s):  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
State Energy ◽  
Energy Levels ◽  
Bound State ◽  
Screen Coulomb Potential ◽  
Normalization Constant ◽  
Angular Momentum State ◽  
Good Agreement

Using improved approximate schemes for centrifugal term and the singular factor 1/r appearing in potential itself, we solve the Schrödinger equation with the screen Coulomb potential for arbitrary angular momentum state l. The bound state energy levels are obtained. A closed form of normalization constant of the wave functions is also found. The numerical results show that our results are in good agreement with those obtained by other methods. The key issue is how to treat two singular points in this quantum system.

A new determination of the parameters of the optimized Heine–Abarenkov potential for 27 elements

1976 ◽  
Vol 54 (23) ◽  
pp. 2348-2354 ◽  
Author(s):  
E. R. Cowley
Keyword(s):  
Schrödinger Equation ◽  
Numerical Integration ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Inhomogeneity Correction ◽  
Radial Schrödinger Equation

We have calculated the energy levels of the truncated Coulomb potential using numerical integration of the radial Schrödinger equation, rather than interpolation in tables. The results are used to give the parameters of the optimized Heine–Abarenkov potential for 27 elements. Various methods of weighting other contributions to the potential in the solid are used, and the inhomogeneity correction introduced by Ballentine and Gupta is discussed.

A Hill-determinant approach to symmetric double-well potentials in two dimensions

1995 ◽  
Vol 73 (9-10) ◽  
pp. 632-637 ◽  
Author(s):  
M. R. M. Witwit ◽  
J. P. Killingbeck
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Dimensional Space ◽  
Energy Levels ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Degenerate Eigenvalues ◽  
Double Well Potential ◽  
Range Of Values

Energy levels of the Schrödinger equation for a double-well potential V(x,y;Z2,λ) = −Z2[x2 + y2] + λ[axxx4 + 2axyx2y2 + ayyy4] in two-dimensional space are calculated, using a Hill-determinant approach for several eigenstates and a range of values of λ and Z2. Special emphasis is placed on the larger values of Z2, for which the eigenvalues for different states have almost degenerate eigenvalues.

scholarly journals METODE ELEMEN HINGGA UNTUK PENYELESAIAN PERSAMAAN SCHRÖDINGER ATOM HIDROGENIK

2006 ◽  
Vol 7 (1) ◽  
pp. 11-23
Author(s):  
Paken Pandiangan ◽  
Supriyadi Supriyadi ◽  
A Arkundato
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Hydrogen Atom ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Wave Functions ◽  
Radial Wave ◽  
Action Integral ◽  
Method Approach

The research computed the energy levels and radial wave functions of the  Hydrogen Atom. The method used for computation was FEM (finite element method). Using the variational method approach, FEM was applied to the action integral of  Schrödinger equation. This lead to the eigenvalue equation in the form of  global matrix equation. The results of computation were depended on boundary of the action integral of Schrödinger equation and number of elements. For boundary 0 - 100a0 and 100 elements,  they were the realistic and best choice of computation to the closed  analytic results. The computation of first five energy levels resulted E1 = -0.99917211 R∞, E2 = -0.24984445 R∞, E3 = -0.11105532 R∞,           E4 = -0.06247405 R∞ and  E5 = -0.03998598 R∞ where 1 R∞ = 13.6 eV. They had relative error under 0.1% to the analytic results.  

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 The noncommutative Coulomb potential

2021 ◽  
pp. 2150094
Author(s):  
B. C. Wang ◽  
E. C. Brenag ◽  
R. G. G. Amorim ◽  
V. C. Rispoli ◽  
S. C. Ulhoa
Keyword(s):  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Potential Problem ◽  
Energy Levels ◽  
Three Dimensional

In this work, we analyze the noncommutative three-dimensional Coulomb potential problem. For this purpose, we used the Kustaanheimo–Stiefel mapping to write the Schrödinger equation for Coulomb potential in a solvable way. Then, the noncommutative hydrogen-like atoms were treated, and their energy levels were found. In addition, we estimate a bound for the noncommutativity parameter.

scholarly journals Spin averaged mass spectrum of heavy quarkonium via asymptotic iteration method

2019 ◽  
Vol 97 (12) ◽  
pp. 1342-1348
Author(s):  
Halil Mutuk
Keyword(s):  
Experimental Data ◽  
Mass Spectrum ◽  
Schrödinger Equation ◽  
Iteration Method ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Wave Functions ◽  
Asymptotic Iteration Method ◽  
Heavy Quarkonium ◽  
Theoretical Studies

In this paper we solved Schrödinger equation with Song–Lin potential by using asymptotic iteration method (AIM). We obtained spin-averaged energy levels and wave functions of charmonium and bottomonium via AIM. Obtained results agree well with available experimental data and other theoretical studies.

Schrödinger equation for the two-dimensional Coulomb potential

1974 ◽  
Vol 9 (6) ◽  
pp. 2617-2624 ◽  
Author(s):  
O. Atabek ◽  
C. Deutsch ◽  
M. Lavaud
Keyword(s):  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Two Dimensional

scholarly journals Schrödinger equation of a particle in a uniformly accelerated frame and the possibility of a new kind of quanta

2015 ◽  
Vol 30 (38) ◽  
pp. 1550182 ◽  
Author(s):  
Sanchari De ◽  
Sutapa Ghosh ◽  
Somenath Chakrabarty
Keyword(s):  
Exact Solution ◽  
Hydrogen Atom ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Minkowski Spacetime ◽  
Quantum Harmonic Oscillator ◽  
One Dimensional ◽  
Spacetime Geometry

In this paper, we have developed a formalism to obtain the Schrödinger equation for a particle in a frame undergoing a uniform acceleration in an otherwise flat Minkowski spacetime geometry. We have presented an exact solution of the equation and obtained the eigenfunctions and the corresponding eigenvalues. It has been observed that the Schrödinger equation can be reduced to a one-dimensional hydrogen atom problem. Whereas, the quantized energy levels are exactly identical with that of a one-dimensional quantum harmonic oscillator. Hence, considering transitions, we have predicted the existence of a new kind of quanta, which will either be emitted or absorbed if the particles get excited or de-excited, respectively.

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