scholarly journals Evaluated Excited-State Time-Independent Correlation Function and Eigenfunction of the Harmonics Oscillator Cosine Asymmetric Potential via Numerical Shooting Method

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Artit Hutem ◽  
Piyarut Moonsri
Keyword(s):  
Correlation Function ◽  
Density Fluctuation ◽  
Shooting Method ◽  
State Energy ◽  
Energy Eigenvalue ◽  
Computational Effort ◽  
Atomic Density ◽  
Excite State ◽  
Numerical Shooting Method ◽  
Problem Comparison

We aimed to evaluate the ground-state and excite-state energy eigenvalue (En), wave function, and the time-independent correlation function of the atomic density fluctuation of a particle under the harmonics oscillator Cosine asymmetric potential (Saad et al. 2013). Instead of using the 6-point kernel of 4 Green’s function (Cherroret and Skipetrov, 2008), averaged over disorder, we use the numerical shooting method (NSM) to solve the Schrödinger equation of quantum mechanics system with Cosine asymmetric potential. Since our approach does not use complicated formulas, it requires much less computational effort when compared to the Green functions techniques (Cherroret and Skipetrov, 2008). We show that the idea of the program of evaluating time-independent correlation function of atomic density is underdamped motion for the Cosine asymmetric potential from the numerical shooting method of this problem. Comparison of the time-independent correlation function obtained from numerical shooting method by Boonchui and Hutem (2012) and correlation function experiment by Kasprzak et al. (2008). We show the intensity of atomic density fluctuation (δn(x)=n~(x)-m~(x)) in harmonics oscillator Cosine asymmetric potential by numerical shooting method.

scholarly journals Excited-State Energy Eigenvalue Evaluation of the Quantum Mechanical Potential V(x)=½mω2x2+μx3 via Numerical Shooting Method

2016 ◽  
Vol 855 ◽  
pp. 184-187
Author(s):  
Nonglux Sriboonrueang ◽  
Sanit Suwanwong ◽  
Artit Hutem
Keyword(s):  
Wave Function ◽  
Excited State ◽  
Single Particle ◽  
Shooting Method ◽  
State Energy ◽  
Energy Eigenvalue ◽  
Quantum Mechanical ◽  
Excited State Energy ◽  
Energy Eigenvalues ◽  
Numerical Shooting Method

The paper deals with eigenvalues excited-state energy eigenvalues and wave-function of a particle under harmonics oscillator asymmetric potential using numerical shooting method. The numerical shooting method is generally regarded as one of the most efficient methods that give very accurate results because it integrates the Schrodinger equation directly, though in the numerical sense. If the value of parameter μ is small the energy eigenvalues of single particle will large and the parameter μ large the energy eigenvalues of single particle will small.

scholarly journals Numerical Solution of SDRE Control Problem – Comparison of the Selected Methods

2020 ◽  
Vol 45 (2) ◽  
pp. 79-95
Author(s):  
Krzysztof Hałas ◽  
Eugeniusz Krysiak ◽  
Tomasz Hałas ◽  
Sławomir Stępień
Keyword(s):  
Control Systems ◽  
Riccati Equation ◽  
Computational Effort ◽  
Linear Control ◽  
Algebraic Riccati Equation ◽  
Linear Control Systems ◽  
Nonlinear Constraints ◽  
State Dependent ◽  
Suboptimal Solution ◽  
Problem Comparison

AbstractMethods for solving non-linear control systems are still being developed. For many industrial devices and systems, quick and accurate regulators are investigated and required. The most effective and promising for nonlinear systems control is a State-Dependent Riccati Equation method (SDRE). In SDRE, the problem consists of finding the suboptimal solution for a given objective function considering nonlinear constraints. For this purpose, SDRE methods need improvement.In this paper, various numerical methods for solving the SDRE problem, i.e. algebraic Riccati equation, are discussed and tested. The time of computation and computational effort is presented and compared considering selected nonlinear control plants.

Size-dependent electronic and optical properties in zinc-blende InGaN/GaN multilayer spherical quantum dot

2017 ◽  
Vol 26 (03) ◽  
pp. 1750035 ◽  
Author(s):  
S. Ortakaya ◽  
M. Kirak ◽  
A. Guldeste
Keyword(s):  
Optical Properties ◽  
Quantum Dot ◽  
Shooting Method ◽  
Energy Eigenvalue ◽  
Refractive Index Change ◽  
Eigenvalues And Eigenfunctions ◽  
Size Dependent ◽  
Spherical Quantum Dot ◽  
Mass Approximation ◽  
Zinc Blende

A theoretical investigation of the binding energy, the radial probability distribution and optical properties (absorption coefficient (AC) and refractive index change (RIC)) of InGaN/GaN multilayer quantum dot (QD) is presented. The calculations are performed within the effective-mass approximation. A shooting method is presented to obtain numerical values for the eigenvalues and eigenfunctions of the structure. The energy eigenvalue, density of probability and optical absorption are compared for cases without and with impurity. It is also found that the ACs and RICs exhibit blue or redshift with different structure of potential profile. The results indicate that the optical properties can be sensitively adjusted by geometry of structure and the presence of impurity.

Dirac Bound States of the Killingbeck Potential Under External Magnetic Fields

2015 ◽  
Vol 70 (7) ◽  
pp. 499-505 ◽  
Author(s):  
Zahra Sharifi ◽  
Fateme Tajic ◽  
Majid Hamzavi ◽  
Sameer M. Ikhdair
Keyword(s):  
Wave Function ◽  
Magnetic Fields ◽  
Ground State ◽  
Bound States ◽  
State Energy ◽  
Potential Model ◽  
Energy Levels ◽  
Energy Eigenvalue ◽  
Wave Functions ◽  
Ansatz Method

AbstractThe Killingbeck potential model is used to study the influence of the external magnetic and Aharanov–Bohm (AB) flux fields on the splitting of the Dirac energy levels in a 2+1 dimensions. The ground state energy eigenvalue and its corresponding two spinor components wave functions are investigated in the presence of the spin and pseudo-spin symmetric limit as well as external fields using the wave function ansatz method.

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