A simple calculation of 〈1/r2〉 for the hydrogen atom and the three-dimensional harmonic oscillator

1997 ◽  
Vol 65 (11) ◽  
pp. 1118-1119 ◽  
Author(s):  
H. Beker
Keyword(s):  
Hydrogen Atom ◽  
Harmonic Oscillator ◽  
Three Dimensional ◽  
Simple Calculation

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

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.

scholarly journals Klein–Gordon particle near RN black hole, generalized sl(2) algebra and harmonic oscillator energy

2019 ◽  
Vol 34 (31) ◽  
pp. 1950196
Author(s):  
J. Sadeghi ◽  
M. R. Alipour
Keyword(s):  
Differential Equation ◽  
Information Theory ◽  
Black Hole ◽  
Energy Spectrum ◽  
Harmonic Oscillator ◽  
Three Dimensional ◽  
The Other ◽  
Thermodynamical Properties ◽  
Heun Functions ◽  
Klein Gordon

In this paper, we consider Klein–Gordon particle near Reissner–Nordström black hole. The symmetry of such a background led us to compare the corresponding Laplace equation with the generalized Heun functions. Such relations help us achieve the generalized [Formula: see text] algebra and some suitable results for describing the above-mentioned symmetry. On the other hand, in case of [Formula: see text], which is near the proximity black hole, we obtain the energy spectrum. When we compare the equation of RN background with Laguerre differential equation, we show that the obtained energy spectrum is same as the three-dimensional harmonic oscillator. So, finally we take advantage of harmonic oscillator energy and make suitable partition function. Such function help us to obtain all thermodynamical properties of black hole. Also, the structure of obtained entropy lead us to have some bit and information theory in the RN black hole.

A POINT-LIKE PICTURE OF THE HYDROGEN ATOM

2004 ◽  
Vol 15 (10) ◽  
pp. 1367-1376
Author(s):  
F. FAGHIHI ◽  
A. JANGJOO ◽  
M. KHANI
Keyword(s):  
Wave Function ◽  
Simple Model ◽  
Hydrogen Atom ◽  
Basic Principle ◽  
Correspondence Principle ◽  
Three Dimensional ◽  
Closed Shell ◽  
Dimensional Shape ◽  
Three Dimensional Shape ◽  
Probability Wave

A point-like picture of the Schrödinger solution for hydrogen atom is worked to emphasize that "point-like particles" may describe as "probability wave function". In each case, the three-dimensional shape of the |Ψnlm(rn, cos θ)|2 is plotted and the paths of the point-like electron (it is better to say reduced mass of the pair particles) are described in each closed shell. Finally, the orbital shape of the molecules are given according to the present simple model. In our opinion, "interpretations of the Correspondence Principle", which is a basic principle in all elementary quantum text, seems to be reviewed again!

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.

Sign in / Sign up

Export Citation Format

Share Document