Eigensolutions and theoretic quantities under the nonrelativistic wave equation

2020 ◽  
Vol 19 (02) ◽  
pp. 2050007
Author(s):  
C. A. Onate ◽  
L. S. Adebiyi ◽  
D. T. Bankole
Keyword(s):  
Wave Function ◽  
Energy Equation ◽  
Radial Wave Function ◽  
Tsallis Entropy ◽  
Radial Wave ◽  
Energy Eigenvalues ◽  
Screening Parameter ◽  
Radial Schrödinger Equation ◽  
Information Energy ◽  
Uvarov Method

The radial Schrödinger equation was solved with the combination of three important potentials with [Formula: see text] as deformed parameter via the parametric Nikiforov–Uvarov method and the energy equation as well as the corresponding normalized radial wave function were obtained in close and compact form. The energy equation obtained was used to study eight molecules. The effect of the deformed parameter on energy eigenvalues was also studied numerically. The subset of the combined potential was also studied numerically and the results were found to be in agreement with the previous results. To extend the application of our work, the wave function obtained was used to calculate some theoretic quantities such as the Tsallis entropy, Rényi entropy and information energy. By putting the Tsallis index to 2, we deduced the information energy from Tsallis entropy. Finally, the effect of the deformed parameter and screening parameter, respectively, on the theoretic quantities were also studied.

scholarly journals Vibrational energies of some diatomic molecules for a modified and deformed potential

2021 ◽  
Author(s):  
C. A. Onate ◽  
I. B. Okon ◽  
M. C. Onyeaju ◽  
O. Ebomwonyi
Keyword(s):  
Energy Equation ◽  
Potential Model ◽  
Radial Wave Function ◽  
Expectation Values ◽  
Radial Wave ◽  
Molecular Potential ◽  
Lithium Dimer ◽  
Sodium Dimer ◽  
Vibrational Energies ◽  
Uvarov Method

Abstract A molecular potential model is proposed and the solutions of the radial Schrӧdinger equation in the presence of the proposed potential is obtained. The energy equation and its corresponding radial wave function are calculated using the powerful parametric Nikiforov-Uvarov method. The energies of cesium dimer for different quantum states were numerically obtained for both negative and positive values of the deformed and adjustable parameters. The results for sodium dimer and lithium dimer were calculated numerically using their respective spectroscopic parameters. The calculated values for the three molecules are in excellent agreement with the observed values. Finally, we calculated different expectation values and examined the effects of the deformed and adjustable parameters on the expectation values.

scholarly journals Vibrational energies of some diatomic molecules for a modified and deformed potential

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
C. A. Onate ◽  
I. B. Okon ◽  
M. C. Onyeaju ◽  
O. Ebomwonyi
Keyword(s):  
Energy Equation ◽  
Potential Model ◽  
Radial Wave Function ◽  
Expectation Values ◽  
Radial Wave ◽  
Molecular Potential ◽  
Lithium Dimer ◽  
Sodium Dimer ◽  
Vibrational Energies ◽  
Uvarov Method

AbstractA molecular potential model is proposed and the solutions of the radial Schrӧdinger equation in the presence of the proposed potential is obtained. The energy equation and its corresponding radial wave function are calculated using the powerful parametric Nikiforov–Uvarov method. The energies of cesium dimer for different quantum states were numerically obtained for both negative and positive values of the deformed and adjustable parameters. The results for sodium dimer and lithium dimer were calculated numerically using their respective spectroscopic parameters. The calculated values for the three molecules are in excellent agreement with the observed values. Finally, we calculated different expectation values and examined the effects of the deformed and adjustable parameters on the expectation values.

scholarly journals STUDY OF THE η-7Be INTERACTION NEAR THRESHOLD IN p-6Li FUSION

2009 ◽  
Vol 18 (05n06) ◽  
pp. 1383-1388
Author(s):  
N. J. UPADHYAY ◽  
N. G. KELKAR ◽  
K. P. KHEMCHANDANI ◽  
B. K. JAIN
Keyword(s):  
Wave Function ◽  
Final State Interaction ◽  
Radial Wave Function ◽  
State Interaction ◽  
Nuclear Medium ◽  
Final State ◽  
Radial Wave ◽  
Near Threshold

We present a calculation for η production in the p-6Li fusion near threshold including the η-7Be final state interaction (FSI). We consider the 6Li and 7Be nuclei as α-d and α-3He clusters respectively. The calculations are done for the lowest states of 7 Be with [Formula: see text] resulting from the L = 1 radial wave function. The η-7Be interaction is incorporated through the η-7BeT–matrix, constructed from the medium modified matrices for the η-3He and η-α systems. These medium modified matrices are obtained by solving few body equations, where the scattering in nuclear medium is taken into account.

Expansion of Radial Wave Function of d or f Electrons and the Shifts of Crystal Field Spectra I. General Theory

1988 ◽  
Vol 9 (3) ◽  
pp. 291-297 ◽  
Author(s):  
Ma Dong-ping ◽  
Zheng Xi-te ◽  
Xu Yi-sun ◽  
Zhang Zheng-gang
Keyword(s):  
Wave Function ◽  
General Theory ◽  
Crystal Field ◽  
Radial Wave Function ◽  
Radial Wave

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 Bound State Solutions of the Hua Potential within the Framework of Two Approximations Scheme

2021 ◽  
Vol 3 (3) ◽  
pp. 38-41
Author(s):  
E. B. Ettah ◽  
P. O. Ushie ◽  
C. M. Ekpo
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Energy Equation ◽  
Bound State ◽  
S Wave ◽  
Angular Momenta ◽  
Special Cases ◽  
Uvarov Method

In this paper, we solve analytically the Schrodinger equation for s-wave and arbitrary angular momenta with the Hua potential is investigated respectively. The wave function as well as energy equation are obtained in an exact analytical manner via the Nikiforov Uvarov method using two approximations scheme. Some special cases of this potentials are also studied.

Asymptotic of the deuteron wave function in the coordinate representation and the charge deuteron form factor at large momentums

2021 ◽  
pp. 2150085
Author(s):  
V. I. Zhaba
Keyword(s):  
Wave Function ◽  
Form Factor ◽  
Deuteron Wave Function ◽  
Radial Wave Function ◽  
Nucleon Nucleon ◽  
Radial Wave ◽  
Nucleon Potential ◽  
Coordinate Representation ◽  
Deuteron Form Factor ◽  
The Difference

Numerical modeling of the deuteron wave function in the coordinate representation for the phenomenological nucleon–nucleon potential Argonne v18 has been performed. For this purpose, the asymptotic behavior of the radial wave function has been taken into account near the origin of coordinates and at infinity. The charge deuteron form factor [Formula: see text], depending on the transmitted momentums up to [Formula: see text], has been calculated employing five models for the deuteron wave function. A characteristic difference in calculations of [Formula: see text] is observed near the positions of the first and second zero. The difference between the obtained values for [Formula: see text] form factor has been analyzed using the values of the ratios and differences for the results. Obtained outcomes for charge deuteron form factor at large momentums may be a prediction for future experimental data.

M-SCHEME CLUSTER-ORBITAL SHELL MODEL APPROACH FOR NEUTRON-RICH SYSTEMS

2009 ◽  
Vol 24 (11n13) ◽  
pp. 1009-1012
Author(s):  
HIROSHI MASUI ◽  
KIYOSHI KATŌ ◽  
KIYOMI IKEDA
Keyword(s):  
Wave Function ◽  
Shell Model ◽  
Oxygen Isotopes ◽  
Radial Wave Function ◽  
Radial Wave ◽  
Gaussian Functions ◽  
Model Formalism ◽  
Model Approach

We developed an m-scheme approach of the cluster-orbital shell model formalism. The radial wave function is treated as the super position of the Gaussian functions with different width parameters. Energies and r.m.s. radii of oxygen isotopes are studied.

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