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

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.

Confined quantum systems: The parabolically confined hydrogen atom

1998 ◽  
Vol 31 (19) ◽  
pp. 4493-4520 ◽  
Author(s):  
D S Krähmer ◽  
W P Schleich ◽  
V P Yakovlev
Keyword(s):  
Hydrogen Atom ◽  
Quantum Systems ◽  
Confined Quantum Systems

scholarly journals Symmetries of Anisotropic Harmonic Oscillators with Rational Ratios of Frequencies and their Relations to U(N) and O(N+1)

2019 ◽  
Vol 7 ◽  
pp. 18
Author(s):  
Dennis Bonatsos ◽  
C. Daskaloyannis ◽  
P. Kolokotronis
Keyword(s):  
Hydrogen Atom ◽  
Harmonic Oscillator ◽  
Harmonic Oscillators ◽  
The Past

The concept of bisection of a harmonic oscillator or hydrogen atom, vised in the past in establishing the connection between U(3) and 0(4), is generalized into multisection (trisection, tetrasection, etc). It is then shown that all symmetries of the N-dimensional anisotropic harmonic oscillator with rational ratios of frequencies (RHO), some of which are underlying the structure of superdeformed and hyperdeformed nuclei, can be obtained from the U(N) symmetry of the corresponding isotropic oscillator with an appropriate combination of multisections. Furthermore, it is seen that bisections of the N-dimensional hydrogen atom, which possesses an 0(N+1) symmetry, lead to the U(N) symmetry, so that further multisections of the hydrogen atom lead to the symmetries of the N-dim RHO. The opposite is in general not true, i.e. multisections of U(N) do not lead to 0(N+1) symmetries, the only exception being the occurence of 0(4) after the bisection of U(3).

The three-dimensional hydrogen atom as a restricted four-dimensional harmonic oscillator

Physica ◽  
1973 ◽  
Vol 65 (2) ◽  
pp. 381-395 ◽  
Author(s):  
M. Boiteux
Keyword(s):  
Hydrogen Atom ◽  
Harmonic Oscillator ◽  
Three Dimensional

Mitochondrial Reconstructions Based on Serial Thick Sections and HVEM

1975 ◽  
Vol 33 ◽  
pp. 286-287
Author(s):  
Jerome J. Paulin
Keyword(s):  
Imaging Techniques ◽  
Three Dimensional ◽  
Posterior Pole ◽  
Dimensional Structure ◽  
Stereo Imaging ◽  
Thin Sections ◽  
Anatomical Features ◽  
The Past ◽  
Cellular Components ◽  
Mitochondrial Reticulum

Within the past decade it has become apparent that HVEM offers the biologist a means to explore the three-dimensional structure of cells and/or organelles. Stereo-imaging of thick sections (e.g. 0.25-10 μm) not only reveals anatomical features of cellular components, but also reduces errors of interpretation associated with overlap of structures seen in thick sections. Concomitant with stereo-imaging techniques conventional serial Sectioning methods developed with thin sections have been adopted to serial thick sections (≥ 0.25 μm). Three-dimensional reconstructions of the chondriome of several species of trypanosomatid flagellates have been made from tracings of mitochondrial profiles on cellulose acetate sheets. The sheets are flooded with acetone, gluing them together, and the model sawed from the composite and redrawn.The extensive mitochondrial reticulum can be seen in consecutive thick sections of (0.25 μm thick) Crithidia fasciculata (Figs. 1-2). Profiles of the mitochondrion are distinguishable from the anterior apex of the cell (small arrow, Fig. 1) to the posterior pole (small arrow, Fig. 2).

scholarly journals Simulation of three-dimensional quantum systems with projected entangled-pair states

2021 ◽  
Vol 103 (20) ◽  
Author(s):  
Patrick C. G. Vlaar ◽  
Philippe Corboz
Keyword(s):  
Three Dimensional ◽  
Quantum Systems
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