scholarly journals The Simplest Meijer's G-Function G0,11,0 as the Radial Functions of the Hydrogen Atom

2015 ◽  
Vol 14 ◽  
pp. 28-32
Author(s):  
A. Pishkoo
Keyword(s):  
Hydrogen Atom ◽  
Harmonic Oscillator ◽  
Ground State ◽  
Operator Method ◽  
Radial Functions ◽  
Simple Harmonic Oscillator

The purpose of this paper is to show that how the sub-family of Meijer's G-functions, G0,11,0, deduces all the radial states of the Hydrogen atom. By introducing two postulates and using operator method similar with the method used for the simple harmonic oscillator we obtain all the excited radial states of the Hydrogen atom from the ground state. It is just needed to use two properties of Meijer's G-functions.

Harmonic Oscillators with Nonlinear Damping

2017 ◽  
Vol 27 (11) ◽  
pp. 1730037 ◽  
Author(s):  
J. C. Sprott ◽  
W. G. Hoover
Keyword(s):  
Dynamical Systems ◽  
Harmonic Oscillator ◽  
Strange Attractor ◽  
Nonlinear Damping ◽  
Harmonic Oscillators ◽  
Coexisting Attractors ◽  
Simple Harmonic Oscillator ◽  
Interesting Behavior

Dynamical systems with special properties are continually being proposed and studied. Many of these systems are variants of the simple harmonic oscillator with nonlinear damping. This paper characterizes these systems as a hierarchy of increasingly complicated equations with correspondingly interesting behavior, including coexisting attractors, chaos in the absence of equilibria, and strange attractor/repellor pairs.

Discussion of several analytical approximate expressions for the eigenvalues of the bounded harmonic oscillator and hydrogen atom

1983 ◽  
Vol 24 (2) ◽  
pp. 169-184 ◽  
Author(s):  
Gustavo A. Arteca ◽  
Sergio A. Maluendes ◽  
Francisco M. Fernández ◽  
Eduardo A. Castro
Keyword(s):  
Hydrogen Atom ◽  
Harmonic Oscillator ◽  
Approximate Expressions

Propagator for the simple harmonic oscillator

1998 ◽  
Vol 66 (11) ◽  
pp. 1022-1024 ◽  
Author(s):  
Nora S. Thornber ◽  
Edwin F. Taylor
Keyword(s):  
Harmonic Oscillator ◽  
Simple Harmonic Oscillator

Constructing physical systems with dynamical symmetry

2014 ◽  
Vol 92 (4) ◽  
pp. 335-340
Author(s):  
Yan Li ◽  
Fu-Lin Zhang ◽  
Rui-Juan Gu ◽  
Jing-Ling Chen ◽  
L.C. Kwek
Keyword(s):  
Hydrogen Atom ◽  
Harmonic Oscillator ◽  
Dynamical Symmetry ◽  
Algebraic Method ◽  
Quantum Systems ◽  
Physical Systems ◽  
Generalized Systems ◽  
Dependent Mass ◽  
Position Dependent Mass

An approach to constructing quantum systems with dynamical symmetry is proposed. As examples, we construct generalized systems of the hydrogen atom and harmonic oscillator, which can be regarded as the systems with position-dependent mass. They have symmetries that are similar to the corresponding ones, and can be solved by using the algebraic method. We also exhibit an example of the method applied to the noncentral field.

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