Evaluate correlation function, wave function and energy of the harmonics oscillator hyperbolic secant-cosine rational asymmetric potential via numerical shooting method

2014 ◽  
Vol 8 ◽  
pp. 721-730
Author(s):  
Artit Hutem
Keyword(s):  
Wave Function ◽  
Correlation Function ◽  
Shooting Method ◽  
Numerical Shooting Method

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.

Density correlation function of a superlattice with wave function overlap

1988 ◽  
Vol 196 (1-3) ◽  
pp. 487-493 ◽  
Author(s):  
R.Q. Yang ◽  
X.J. Lu ◽  
X.L. Lei ◽  
L.M. Xie ◽  
C.H. Tsai
Keyword(s):  
Wave Function ◽  
Correlation Function ◽  
Density Correlation ◽  
Density Correlation Function

scholarly journals TOWARDS RELIABLE CALCULATIONS OF THE CORRELATION FUNCTION

2007 ◽  
Vol 16 (10) ◽  
pp. 3244-3261 ◽  
Author(s):  
RADOSŁAW MAJ ◽  
STANISŁAW MRÓWCZYŃSKI
Keyword(s):  
Wave Function ◽  
Correlation Function ◽  
Coulomb Interaction ◽  
Relative Motion ◽  
Coulomb Potential ◽  
Center Of Mass ◽  
Relativistic Effects ◽  
Life Time ◽  
Large Domain ◽  
Mass Frame

The correlation function of two identical pions interacting via Coulomb potential is computed for a general case of anisotropic particle's source of finite life time. The effect of halo is taken into account as an additional particle's source of large spatial extension. Due to the Coulomb interaction, the effect of halo is not limited to very small relative momenta but it influences the correlation function in a relatively large domain. The relativistic effects are discussed in detail and it is argued that the calculations have to be performed in the center-of-mass frame of particle's pair where the (nonrelativistic) wave function of particle's relative motion is meaningful. The Bowler–Sinyukov procedure to remove the Coulomb interaction is tested and it is shown to significantly underestimate the source's life time.

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