Rigorous solutions of diatomic molecule oscillator with empirical potential function in phase space

2000 ◽  
Vol 113 (11) ◽  
pp. 4565-4571 ◽  
Author(s):  
Qian-Shu Li ◽  
Jun Lu
Keyword(s):  
Phase Space ◽  
Potential Function ◽  
Diatomic Molecule ◽  
Empirical Potential

Phase-Space Wave Functions of Diatomic System in One-Dimensional Nanomaterials

2011 ◽  
Vol 474-476 ◽  
pp. 1179-1182
Author(s):  
Jun Lu
Keyword(s):  
Phase Space ◽  
Exact Solutions ◽  
Potential Function ◽  
Wave Functions ◽  
Space Representation ◽  
One Dimensional ◽  
Empirical Potential ◽  
Diatomic System ◽  
Phase Space Representation ◽  
Space Wave

The exact solutions of the stationary Schrödinger equations for the diatomic system with an empirical potential function in one-dimensional nanomaterials are solved within the framework of the quantum phase-space representation established by Torres-Vega and Frederick. The wave functions in position and momentum representations can be obtained through the Fourier-like projection transformation from the phase-space wave functions.

ADSORPTION AND DIFFUSION OF Si ON THE Si(001): AN EMPIRICAL POTENTIAL CALCULATION

2002 ◽  
Vol 16 (04) ◽  
pp. 621-629 ◽  
Author(s):  
JUN CAI ◽  
JIAN-SHENG WANG
Keyword(s):  
Potential Function ◽  
Binding Sites ◽  
Surface Adsorption ◽  
First Principle ◽  
Empirical Potential ◽  
First Principle Calculations ◽  
Diffusion Paths ◽  
And Diffusion ◽  
Formation Energies ◽  
Diffusion Activation

A recently developed potential function for covalent materials (Phys. Stat. Sol.B212, 9 (1999)) is used to simulate the surface adsorption, and diffusion of Si adtom and ad-dimer on the Si(001) surface. We calculate the formation energies and diffusion activation energies of several possible binding sites. The predicted stable and metastable configurations and diffusion paths of Si ad-atom and Si ad-dimer on Si(001)-(2×1) surface are in agreement with that from the first principle calculations or experiments.

scholarly journals Scalar field cosmology — geometry of dynamics

2014 ◽  
Vol 11 (02) ◽  
pp. 1460012 ◽  
Author(s):  
Marek Szydłowski ◽  
Orest Hrycyna ◽  
Aleksander Stachowski
Keyword(s):  
Phase Space ◽  
Scalar Field ◽  
Dynamical Systems ◽  
Potential Function ◽  
Structural Stability ◽  
Saddle Points ◽  
Scalar Fields ◽  
Fine Tuning ◽  
Scalar Field Cosmology ◽  
Structurally Stable

We study the Scalar Field Cosmology (SFC) using the geometric language of the phase space. We define and study an ensemble of dynamical systems as a Banach space with a Sobolev metric. The metric in the ensemble is used to measure a distance between different models. We point out the advantages of visualization of dynamics in the phase space. It is investigated the genericity of some class of models in the context of fine tuning of the form of the potential function in the ensemble of SFC. We also study the symmetries of dynamical systems of SFC by searching for their exact solutions. In this context, we stressed the importance of scaling solutions. It is demonstrated that scaling solutions in the phase space are represented by unstable separatrices of the saddle points. Only critical point itself located on two-dimensional stable submanifold can be identified as scaling solution. We have also found a class of potentials of the scalar fields forced by the symmetry of differential equation describing the evolution of the Universe. A class of potentials forced by scaling (homology) symmetries was given. We point out the role of the notion of a structural stability in the context of the problem of indetermination of the potential form of the SFC. We characterize also the class of potentials which reproduces the ΛCDM model, which is known to be structurally stable. We show that the structural stability issue can be effectively used is selection of the scalar field potential function. This enables us to characterize a structurally stable and therefore a generic class of SFC models. We have found a nonempty and dense subset of structurally stable models. We show that these models possess symmetry of homology.

Rotation and vibration of diatomic molecule oscillator with hyperbolic potential function

2005 ◽  
Vol 14 (12) ◽  
pp. 2402-2406 ◽  
Author(s):  
Lu Jun ◽  
Qian Hui-Xian ◽  
Li Liang-Mei ◽  
Liu Feng-Ling
Keyword(s):  
Potential Function ◽  
Diatomic Molecule ◽  
Hyperbolic Potential

Forces in Molecules. III. Analysis of an Empirical Potential Function

1963 ◽  
Vol 39 (12) ◽  
pp. 3316-3321 ◽  
Author(s):  
William L. Clinton ◽  
Sandra D. Frattali
Keyword(s):  
Potential Function ◽  
Empirical Potential
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