Degeneracies of the spherical well, harmonic oscillator and hydrogen atom in arbitrary dimensions

1996 ◽  
Vol 64 (4) ◽  
pp. 430-434 ◽  
Author(s):  
Richard W. Shea ◽  
P. K. Aravind
Keyword(s):  
Hydrogen Atom ◽  
Harmonic Oscillator ◽  
Arbitrary Dimensions

Transformation between a hydrogen atom and a harmonic oscillator of arbitrary dimensions

1997 ◽  
Vol 30 (5) ◽  
pp. 1775-1783 ◽  
Author(s):  
Gao-Jian Zeng ◽  
Shi-Lun Zhou ◽  
Sheng-Mei Ao ◽  
Fa-Sheng Jiang
Keyword(s):  
Hydrogen Atom ◽  
Harmonic Oscillator ◽  
Arbitrary Dimensions

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

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.

ENERGY-DEPENDENT POTENTIAL AND NORMALIZATION OF WAVE FUNCTION

2013 ◽  
Vol 28 (18) ◽  
pp. 1350079 ◽  
Author(s):  
A. BENCHIKHA ◽  
L. CHETOUANI
Keyword(s):  
Wave Function ◽  
Hydrogen Atom ◽  
Harmonic Oscillator ◽  
Path Integral ◽  
Spectral Decomposition ◽  
Wave Functions ◽  
Integral Approach ◽  
Path Integral Approach ◽  
Dependent Potential ◽  
Energy Dependent

The problem of normalization related to energy-dependent potentials is examined in the context of the path integral approach, and a justification is given. As examples, the harmonic oscillator and the hydrogen atom (radial) where, respectively the frequency and the Coulomb's constant depend on energy, are considered and their propagators determined. From their spectral decomposition, we have found that the wave functions extracted are correctly normalized.

WKB quantization rules for three-dimensional confinement

2001 ◽  
Vol 79 (6) ◽  
pp. 939-946 ◽  
Author(s):  
A Sinha ◽  
R Roychoudhury ◽  
Y P Varshni
Keyword(s):  
Hydrogen Atom ◽  
Harmonic Oscillator ◽  
Reasonable Agreement ◽  
Three Dimensional ◽  
Quantum Systems ◽  
The Past ◽  
Two Systems ◽  
Mathematical Techniques ◽  
Confined Quantum Systems ◽  
Quantization Rules

Confined quantum systems have been studied by various authors over the past decades, by using various mathematical techniques. In this work, we derive the WKB quantization rules for quantum systems confined in an impenetrable spherical box of radius r0. We apply the proposed method to two systems explicitly, viz., the confined harmonic oscillator and the confined hydrogen atom. The results are found to be in reasonable agreement with those obtained by other methods. PACS No.: 03.65

Time evolution of a time-dependent inverted harmonic oscillator in arbitrary dimensions

2012 ◽  
Vol 45 (11) ◽  
pp. 115301
Author(s):  
Guang-Jie Guo ◽  
Zhong-Zhou Ren ◽  
Guo-Xing Ju ◽  
Xiao-Yong Guo
Keyword(s):  
Harmonic Oscillator ◽  
Time Evolution ◽  
Time Dependent ◽  
Arbitrary Dimensions
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