An efficient and economical high order method for the numerical approximation of the Schrödinger equation

Liu, Yang; Simos, T. E.

doi:10.1007/s10910-017-0757-5

Cited by 36 publications

(2 citation statements)

References 81 publications

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“…S νσ (θ, ϕ) , (23) where µ >= − (ν − 1) and κ >= 0, S νσ (θ, ϕ) are real or complex spherical harmonics. The case ν = σ = 0 corresponds to the screened central potential.…”

Section: Resultsmentioning

confidence: 99%

“…Several other variants in order to increase both stability and accuracy while calculating the resonance problems and high−lying bound states were proposed. Generalization of the algorithm to an error of arbitrary order [15][16][17][18][19][20][21][22][23][24][25] and extension it for solution of differential equations with more than one−dimension [8,[26][27][28][29][30][31][32][33] form the main framework of the studies. A Numerov−type exponentially fitted method was suggested [18-20, 32, 34-43], accordingly.…”

Section: Introductionmentioning

confidence: 99%

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An efficient approximation for accelerating convergence of the numerical power series. Results for the 1D Schrödinger's equation

Bagci¹,

Guneş²

2021

Preprint

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The numerical matrix Numerov method is used to solve the stationary Schrödinger equation for central Coulomb potentials. An efficient approximation for accelerating the convergence is proposed. The Numerov method is error−prone if the magnitude of grid−size is not chosen properly. A number of rules so far, have been devised. The effectiveness of these rules decrease for more complicated equations. The grid−size that is used for discretization of the Schrödinger's equation is allowed to be variationally for the given boundary conditions. In order to test efficiency of the technique used for accelerating the convergence, the grid-sizes are determined via the optimization procedure performed for each energy state. The results obtained for energy eigenvalues and corresponding eigen−vectors are compared with the literature. It is observed that, once the values of grid−sizes for hydrogen energy eigenvalues are obtained, they can simply be determined for the hydrogen iso−electronic series as, hε(Z) = hε(1)/Z.

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“…S νσ (θ, ϕ) , (23) where µ >= − (ν − 1) and κ >= 0, S νσ (θ, ϕ) are real or complex spherical harmonics. The case ν = σ = 0 corresponds to the screened central potential.…”

Section: Resultsmentioning

confidence: 99%