Solutions with the Model Potential for the Potential Representation Method

2020 ◽  
pp. 149-159
Keyword(s):  
Model Potential ◽  
Representation Method ◽  
Potential Representation

scholarly journals POTENTIAL REPRESENTATION METHOD FOR THE SCHRÖDINGER EQUATION

2011 ◽  
Vol 16 (3) ◽  
pp. 442-450 ◽  
Author(s):  
Arvydas Juozapas Janavičius ◽  
Donatas Jurgaitis ◽  
Sigita Turskienė
Keyword(s):  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Integral Equations ◽  
Schrodinger Equation ◽  
Bound States ◽  
Model Potential ◽  
Variation Of Constants ◽  
Potential Perturbation ◽  
Representation Method ◽  
Potential Representation

A general solution of the Schrödinger equation in the potential representation has been obtained in the form of integral equations. In this representation, the wave function for positive and negative energies or bound states can be expressed as a product of the unperturbed solution for model potential and the function which depends on the additional potential or potential perturbation. Here we have proved that this method is equivalent to the method of variation of constants for negative energies. The linearly independent solutions of Schrödinger equation for harmonic oscillator potential have been obtained for derivation of integral equations, which are used for finding eigenfunctions and eigenvalues for Woods–Saxon potential. Eigenvalues obtained by numerical iterations of these integral equations are in good agreement with results obtained by the discretization method. The kernels of the obtained integral equations are proportional to the perturbation or difference of Woods–Saxon and harmonic oscillator potentials.

MICROSCOPIC CALCULATION OF THE OPTICAL-MODEL POTENTIAL

1974 ◽  
Vol 35 (C5) ◽  
pp. C5-7-C5-7
Author(s):  
J. P. JEUKENNE ◽  
A. LEJEUNE ◽  
C. MAHAUX
Keyword(s):  
Optical Model ◽  
Model Potential ◽  
Microscopic Calculation ◽  
Optical Model Potential

Calculations of Polarizabilities and Their Gradients for Electron Energy-Loss Spectroscopy

2008 ◽  
Vol 73 (11) ◽  
pp. 1509-1524 ◽  
Author(s):  
Ivana Paidarová ◽  
Roman Čurík ◽  
Stephan P. A. Sauer
Keyword(s):  
Energy Loss ◽  
Electron Energy ◽  
Theoretical Models ◽  
Basis Set ◽  
Polarizability Tensor ◽  
Dipole Polarizability ◽  
Perfect Agreement ◽  
Representation Method ◽  
Response Method ◽  
Electron Energy Loss

We illustrate for a set of small hydrocarbons, CH4, C2H4, C3H6 and C3H8, the important role of the electric dipole polarizability tensor and its geometric derivatives in theoretical models of electron energy-loss spectra (EELS). The coupled cluster linear response method together with Sadlej's polarized valence triple zeta basis set of atomic orbitals were used to calculate the polarizabilities and polarizability gradients. Incorporation of these ab initio data into the discrete momentum representation method (DMR) leads to perfect agreement between theory and collision experiments.

scholarly journals Relativistic B-Spline R-Matrix Calculations for Electron Collisions with Ytterbium

Atoms ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 47
Author(s):  
Kathryn R. Hamilton ◽  
Klaus Bartschat ◽  
Oleg Zatsarinny
Keyword(s):  
Experimental Data ◽  
Electron Scattering ◽  
Cross Sections ◽  
Matrix Method ◽  
Model Potential ◽  
Electron Collisions ◽  
R Matrix ◽  
B Spline ◽  
Potential Approach

We have applied the full-relativistic Dirac B-Spline R-matrix method to obtain cross sections for electron scattering from ytterbium atoms. The results are compared with those obtained from a semi-relativistic (Breit-Pauli) model-potential approach and the few available experimental data.

scholarly journals Plutonium complexes in water: new approach to ab initio modeling

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Mikhail V. Ryzhkov ◽  
Andrei N. Enyashin ◽  
Bernard Delley
Keyword(s):  
Quantitative Estimation ◽  
Water Solution ◽  
Geometry Optimization ◽  
Model Potential ◽  
Water Dissociation ◽  
New Approach ◽  
Molecular Systems ◽  
Screening Model ◽  
Solvent Environment ◽  
Structure Calculations

Abstract Geometry optimization and the electronic structure calculations of Pu Z+ complexes (Z = 3–6) in water solution have been performed, within the framework of the DMol3 and Relativistic Discrete-Variational (RDV) methods. For the simulation of Pu Z+ molecular environment in aqueous solution we used 22 and 32 water molecules randomly distributed around cation. To model the effect of bulk solvent environment we used COSMO (Conductor-like Screening Model) potential for water (ε = 78.54). The obtained results showed that this approach allows the modeling of water dissociation and the formation of hydrolysis products. Our previously suggested scheme for the calculation of interaction energies between selected fragments of multi-molecular systems provides the quantitative estimation of the interaction strengths between plutonium in various oxidation states and each ligand in the first and second coordination shells in water solution.

scholarly journals Neuronalis összeköttetések a szomatoszenzoros kérgi área 3b és área 1 kézreprezentációs területén főemlősökben

2016 ◽  
Vol 157 (33) ◽  
pp. 1320-1325
Author(s):  
Emese Pálfi ◽  
Mária Ashaber ◽  
Cory Palmer ◽  
Robert M. Friedman ◽  
Anna W. Roe ◽  
...  
Keyword(s):  
Functional Relationship ◽  
Hand Movement ◽  
Saimiri Sciureus ◽  
Skin Area ◽  
Tract Tracing ◽  
Reciprocal Connections ◽  
Representation Method ◽  
Local Input ◽  
Finger Pad ◽  
Area 3B

Introduction: The close functional relationship between areas 3b and 1 of the somatosensory cortex is based on their reciprocal connections indicating that tactile sensation depends on the interaction of these two areas. Aim: The aim of the authors was to explore this neuronal circuit at the level of the distal finger pad representation. Method: The study was made by bidirectional tract tracing aided by neurophysiological mapping in squirrel monkeys (Saimiri sciureus). Results: Inter-areal connections between the two areas preferred the homologues representations. However, intra-areal connections were formed between the neighboring finger pad representations supporting the physiological observations. Interestingly, the size of the local input area of the injected cortical micro-region, which differed in the two areas, represented the same skin area. Conclusions: The authors propose that intra-areal connections are important in integrating information across fingers, while inter-areal connections are important in maintaining input localization during hand movement. Orv. Hetil., 2016, 157(33), 1320–1325.

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