scholarly journals Connection between quantum systems involving the fourth Painlevé transcendent and k-step rational extensions of the harmonic oscillator related to Hermite exceptional orthogonal polynomial

2016 ◽  
Vol 57 (5) ◽  
pp. 052101 ◽  
Author(s):  
Ian Marquette ◽  
Christiane Quesne
Keyword(s):  
Harmonic Oscillator ◽  
Orthogonal Polynomial ◽  
Quantum Systems ◽  
Painlevé Transcendent

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

scholarly journals Pure Decoherence in Quantum Systems

2004 ◽  
Vol 11 (01) ◽  
pp. 53-61 ◽  
Author(s):  
Robert Alicki
Keyword(s):  
Energy Dissipation ◽  
Elastic Scattering ◽  
Energy Conservation ◽  
Harmonic Oscillator ◽  
Quantum Systems ◽  
Scattering Mechanism ◽  
Linear Coupling

A popular model of decoherence based on the linear coupling to harmonic oscillator heat baths is analysed and shown to be inappropriate in the regime where decoherence dominates over energy dissipation, called pure decoherence regime. The similar mechanism essentially related to the energy conservation implies that, on the contrary to some recent conjectures [21], chaotic environments can be less efficient decoherers than regular ones. Finally, the elastic scattering mechanism is advocated as the simplest source of pure decoherence.

Classical and Mexican hat-type potential energy curve for the hydrogen molecule from a confined Kratzer oscillator

2016 ◽  
Vol 30 (09) ◽  
pp. 1650043
Author(s):  
G. Van Hooydonk
Keyword(s):  
Potential Energy ◽  
Harmonic Oscillator ◽  
Potential Energy Curve ◽  
Molecular Spectroscopy ◽  
Universal Function ◽  
Quantum Systems ◽  
Energy Curve ◽  
Mexican Hat ◽  
Stable Quantum ◽  
Better Than

We review harmonic oscillator theory for closed, stable quantum systems. The H2 potential energy curve (PEC) of Mexican hat-type, calculated with a confined Kratzer oscillator, is better than the Rydberg–Klein–Rees (RKR) H2 PEC. Compared with QM, the theory of chemical bonding is simplified, since a confined Kratzer oscillator can also lead to the long sought for universal function, once called the Holy Grail of Molecular Spectroscopy. This is validated by reducing PECs for different bonds H2, HF, I2, N2 and O2 to a single one. The equal probability for H2, originating either from [Formula: see text] or [Formula: see text], is quantified with a Gauss probability density function. At the Bohr scale, a confined harmonic oscillator behaves properly at the extremes of bound two-nucleon quantum systems.

CONTROL OF QUANTUM SYSTEMS

1999 ◽  
Vol 09 (02) ◽  
pp. 305-324 ◽  
Author(s):  
R. B. PÉREZ ◽  
V. PROTOPOPESCU ◽  
J. L. MUÑOZ-COBO
Keyword(s):  
Harmonic Oscillator ◽  
Quantum Dynamics ◽  
Control Method ◽  
Quantum Systems ◽  
Microscopic Level ◽  
Oscillator System ◽  
Schrödinger’S Equation ◽  
Control Of Quantum Systems ◽  
Schrödinger's Equation

We propose a new control method for systems whose evolution is described by Schrödinger's equation (quantum dynamics). The goal of the control is to induce modifications of observable quantities — with possible effects at mesoscopic or macroscopic levels — by modifying the potential at the microscopic level. We illustrate the feasibility of the approach on a harmonic oscillator system.

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