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.

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

Position-dependent mass Schrödinger equations allowing harmonic oscillator (HO) eigenvalues

2008 ◽  
Vol 108 (15) ◽  
pp. 2906-2913 ◽  
Author(s):  
J. J. Peña ◽  
G. Ovando ◽  
J. Morales ◽  
J. GarcÍa-Ravelo ◽  
C. Pacheco-García
Keyword(s):  
Harmonic Oscillator ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Dependent Mass ◽  
Position Dependent Mass

Quantum systems with effective and time-dependent masses: form-preserving transformations and reality conditions

Open Physics ◽  
2005 ◽  
Vol 3 (4) ◽  
Author(s):  
Axel Schulze-Halberg
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Transport Phenomena ◽  
Quantum Systems ◽  
Time Dependent ◽  
Effective Masses ◽  
Dependent Mass ◽  
Position Dependent Mass

AbstractWe study the time-dependent Schrödinger equation (TDSE) with an effective (position-dependent) mass, relevant in the context of transport phenomena in semiconductors. The most general form-preserving transformation between two TDSEs with different effective masses is derived. A condition guaranteeing the reality of the potential in the transformed TDSE is obtained. To ensure maximal generality, the mass in the TDSE is allowed to depend on time also.

The harmonic oscillator and the position dependent mass Schrödinger equation: isospectral partners and factorization operators

2010 ◽  
Author(s):  
J. Morales ◽  
G. Ovando ◽  
J. J. Peña ◽  
Kurt B. Wolf ◽  
Luis Benet ◽  
...  
Keyword(s):  
Harmonic Oscillator ◽  
Dependent Mass ◽  
Position Dependent Mass

scholarly journals Position-dependent mass quantum systems and ADM formalism

2021 ◽  
Author(s):  
Davood Momeni
Keyword(s):  
Wave Equation ◽  
Phase Space ◽  
Classical System ◽  
Quantum Systems ◽  
Order System ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Dimensional Phase Space ◽  
Dependent Mass ◽  
Position Dependent Mass

The classical Einstein-Hilbert (EH) action for general relativity (GR) is shown to be formally analogous to the classical system with position-dependent mass (PDM) models. The analogy is developed and used to build the covariant classical Hamiltonian as well as defining an alternative phase portrait for GR. The set of associated Hamilton’s equations in the phase space is presented as a first-order system dual to the Einstein field equations. Following the principles of quantum mechanics, I build a canonical theory for the classical general. A fully consistent quantum Hamiltonian for GR is constructed based on adopting a high dimensional phase space. It is observed that the functional wave equation is timeless. As a direct application, I present an alternative wave equation for quantum cosmology. In comparison to the standard Arnowitt-Deser-Misner(ADM) decomposition and quantum gravity proposals, I extended my analysis beyond the covariant regime when the metric is decomposed into the 3+13+1 dimensional ADM decomposition. I showed that an equal dimensional phase space can be obtained if one applies ADM decomposed metric.

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