scholarly journals Removal of ordering ambiguity for a class of position dependent mass quantum systems with an application to the quadratic Liénard type nonlinear oscillators

2015 ◽  
Vol 56 (1) ◽  
pp. 012103 ◽  
Author(s):  
V. Chithiika Ruby ◽  
V. K. Chandrasekar ◽  
M. Senthilvelan ◽  
M. Lakshmanan
Keyword(s):  
Nonlinear Oscillators ◽  
Quantum Systems ◽  
Dependent Mass ◽  
Position Dependent Mass

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.

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.

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.

scholarly journals Displacement operator for quantum systems with position-dependent mass

2011 ◽  
Vol 84 (5) ◽  
Author(s):  
R. N. Costa Filho ◽  
M. P. Almeida ◽  
G. A. Farias ◽  
J. S. Andrade
Keyword(s):  
Quantum Systems ◽  
Displacement Operator ◽  
Dependent Mass ◽  
Position Dependent Mass
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