Renormalized Numerov method applied to eigenvalue equations: extension to include single derivative terms and a variety of boundary conditions

Leroy, J. P.; Wallace, R.

doi:10.1021/j100256a023

Cited by 37 publications

(20 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This take us to solve numerically the radial Schrödinger equation, Eq. (3), by using the Numerov method [35,36,37,38,39,40]. The algorithm was implemented in a program developed by the authors using C ++ language.…”

Section: Planar Physics and The Ln(r) Potentialmentioning

confidence: 99%

How the inter-electronic potential Ansätze affect the bound state solutions of a planar two-electron quantum dot model

Caruso

Oguri

Silveira

2019

Physica E: Low-dimensional Systems and Nanostructures

View full text Add to dashboard Cite

The model of a two-electron quantum dot, confined to move in a two dimensional flat space, in the presence of an external harmonic oscillator potential, is revisited for a specific purpose. Indeed, eigenvalues and eigenstates of the bound state solutions are obtained for any oscillation frequency considering both the 1/r and ln r Ansätze for inter-electronic Coulombic-like potentials in 2D. Then, it is pointed out that the significative difference between measurable quantities predicted from these two potentials can shed some light on the problem of space dimensionality as well as on the physical nature of the potential itself.

show abstract

Section: Planar Physics and The Ln(r) Potentialmentioning

confidence: 99%

How the inter-electronic potential Ansätze affect the bound state solutions of a planar two-electron quantum dot model

Caruso

Oguri

Silveira

2019

Physica E: Low-dimensional Systems and Nanostructures

View full text Add to dashboard Cite

show abstract

“…(19) is solved using the renormalized Numerov method [54]. The sum of σ A and σ P computed using Eqs.…”

Section: Theorymentioning

confidence: 99%

Ionization in collisions between metastable hydrogen atoms

et al. 2012

View full text Add to dashboard Cite

Associative and Penning ionization cross sections are calculated for collisions between metastable hydrogen 2s atoms at thermal energies. Cross sections for deuterium 2s collisions are also reported. The associative ionization cross sections behave as E −1 for collision energy E, in agreement with an existing experiment. The Penning ionization cross sections dominate for all energies and are found to follow the E −2/3 behavior that was predicted in previous work for the total ionization cross section. The magnitudes of our theoretical associative ionization cross sections for H(2s) + H(2s) collisions are between two and four times larger than the experimental data.

show abstract

“…Example applications can be found in solid state physics [32], kinetic mechanisms [33,34], thermal dynamics 1351, and spectrum theory [36,37]. Although this model cannot be solved analytically, numerical methods such as the Numerov method [4] can give precise results.…”

Section: The Anharmonic Oscillatormentioning

confidence: 99%

The multireference constant denominator perturbation theory for one‐particle systems and its application to the anharmonic oscillator

Lan

Cullen

1990

Int J of Quantum Chemistry

View full text Add to dashboard Cite

In this paper a multireference constant denominator perturbation theory (CDPT) is developed to reduce incomplete basis set errors arising when solving the Schrödinger equation with a finite basis set. The advantage of this method is that very few basis functions are needed, and all calculations if carried out to high enough order in the perturbation treatment effectively use a complete basis set. As a first step the theory has been restricted to one‐particle Hamiltonians and applied to the anharmonic oscillator to study the convergence properties. For perturbation calculations carried out to fifth order, results from Pade approximates show an improvement in accuracy of between one and three orders of magnitude.

show abstract

Renormalized Numerov method applied to eigenvalue equations: extension to include single derivative terms and a variety of boundary conditions

Cited by 37 publications

References 5 publications

How the inter-electronic potential Ansätze affect the bound state solutions of a planar two-electron quantum dot model

How the inter-electronic potential Ansätze affect the bound state solutions of a planar two-electron quantum dot model

Ionization in collisions between metastable hydrogen atoms

The multireference constant denominator perturbation theory for one‐particle systems and its application to the anharmonic oscillator

Contact Info

Product

Resources

About