Excited-State Energy Eigenvalue Evaluation of the Quantum Mechanical Potential V(x)=½mω2x2+μx3 via 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.

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

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.