The Schrödinger and Riccati Equations

Vega

Theoretical Chemistry Accounts: Theory, Computation, and Modeli

2001

The hydrogen-ion molecule has been used as a test system for the application of the SchroÈ dinger± Riccati formulation to molecular calculations. Some of the points discussed are the characteristics (quasiconstancy of the local energies, size, number of points) of the sampling region to be chosen, the dependence on the starting function, the precision of the calculations, and the excellent behaviour of the predicted function (by comparison to an accurate function).

“…The details of the derivation of the SRE may be found in previous work [1,2] and here we just summarize the actual procedure for numerical calculations.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Section: Theoretical Backgroundmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Molecular Schr�dinger-Riccati calculations. Test for the hydrogen-ion molecule

Vega

Theoretical Chemistry Accounts: Theory, Computation, and Modeli

2001

International Journal of Mathematics and Mathematical Sciences

“…This paper aims to solve a FDE called fractional-order Riccati differential equation, one of the important equations in the family of FDEs. The Riccati equations play an important role in engineering and applied science [6], especially in quantum mechanics [7] and quantum chemistry [8,9]. Therefore, solutions to the Riccati differential equations are important to scientists and engineers.…”

Section: Introductionmentioning

confidence: 99%

Legendre Wavelet Operational Matrix Method for Solution of Riccati Differential Equation

Balaji

2014

A Legendre wavelet operational matrix method (LWM) is presented for the solution of nonlinear fractional-order Riccati differential equations, having variety of applications in quantum chemistry and quantum mechanics. The fractional-order Riccati differential equations converted into a system of algebraic equations using Legendre wavelet operational matrix. Solutions given by the proposed scheme are more accurate and reliable and they are compared with recently developed numerical, analytical, and stochastic approaches. Comparison shows that the proposed LWM approach has a greater performance and less computational effort for getting accurate solutions. Further existence and uniqueness of the proposed problem are given and moreover the condition of convergence is verified.

Schrödinger–Riccati equation: Feasibility study for the He‐isoelectronic series

Vega

Int J of Quantum Chemistry

2005

Self Cite

ABSTRACT:The Schrö dinger-Riccati equation has been applied to the study of some systems of the He-isoelectronic series. The statistical analysis of the local ratios of the predicted function over an accurate function yields, with a sample mean of 1.000, the following confidence intervals (at a 99% level of confidence) for the true population means: He I, 0.0013 (for 24,896 points); Li II, 0.0015 (for 29,354 points); Be III, 0.0018 (for 31,290 points); C V, 0.0024 (for 28,639 points); and O VII, 0.0058 (for 23,784 points).