scholarly journals Quantum mechanics of Drude oscillators with full Coulomb interaction

2016 ◽  
Vol 94 (11) ◽  
Author(s):  
M. Sadhukhan ◽  
Frederick R. Manby
Keyword(s):  
Quantum Mechanics ◽  
Coulomb Interaction ◽  
Drude Oscillators

Bound state solution of the Schrodinger equation for the Woods–Saxon potential plus coulomb interaction by Nikiforov–Uvarov and supersymmetric quantum mechanics methods

2021 ◽  
pp. 2150023
Author(s):  
Enayatolah Yazdankish
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Coulomb Interaction ◽  
Schrodinger Equation ◽  
Energy Eigenvalue ◽  
Bound State ◽  
Repulsive Interaction ◽  
Saxon Potential ◽  
Special Cases ◽  
Supersymmetry Quantum Mechanics

The generalized Woods–Saxon potential plus repulsive Coulomb interaction is considered in this work. The supersymmetry quantum mechanics method is used to get the energy spectrum of Schrodinger equation and also the Nikiforov–Uvarov approach is employed to solve analytically the Schrodinger equation in the framework of quantum mechanics. The potentials with centrifugal term include both exponential and radial terms, hence, the Pekeris approximation is considered to approximate the radial terms. By using the step-by-step Nikiforov–Uvarov method, the energy eigenvalue and wave function are obtained analytically. After that, the spectrum of energy is obtained by the supersymmetry quantum mechanics method. The energy eigenvalues obtained from each method are the same. Then in special cases, the results are compared with former result and a full agreement is observed. In the [Formula: see text]-state, the standard Woods–Saxon potential has no bound state, but with Coulomb repulsive interaction, it may have bound state for zero angular momentum.

The nonlinear behaviors of movement of electron in the atoms

2015 ◽  
Vol 29 (12) ◽  
pp. 1550054
Author(s):  
Xiao-Feng Pang
Keyword(s):  
Quantum Mechanics ◽  
Hydrogen Atom ◽  
Coulomb Interaction ◽  
Nonlinear Theory ◽  
Coulomb Potential ◽  
Nonlinear Interaction ◽  
Energy Levels ◽  
Nonlinear Interactions ◽  
Theory Of Motion ◽  
Nonlinear Behaviors

In view of difficulties and questions of quantum mechanics in description of motion of electrons in hydrogen atom, we here established their nonlinear theory of motion based on the true motions of electron and nucleon and the real interactions between them, in which the motion of electron is depicted by a nonlinear Schrödinger equation with a Coulomb potential, the nonlinear interaction b∣φ∣2φ is produced by the change of Coulomb interaction between nucleon and electron due to the motion of nucleon. Thus the natures of the electron are thoroughly changed relative to those in quantum mechanics due to the nonlinear interactions, it not only is stable and localized, but also possesses a wave–corpuscle duality. Meanwhile, if its eigenenergy is still quantized and distributed in accordance with the energy levels, then we can use the new theory to explain perfectly the spectrum features of hydrogen atom, which resembles quantum mechanics, but its sizes of eigenenergy are depressed relative to that in quantum mechanics. This means that the nonlinear interaction enhances the localized and stable nature of the electron. Therefore, the new nonlinear theory is successful and correct to the hydrogen atom.

Quantum Mechanics

2009 ◽  
Author(s):  
Gennaro Auletta ◽  
Mauro Fortunato ◽  
Giorgio Parisi
Keyword(s):  
Quantum Mechanics
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