Measuring the accuracy of the solution subspace obtained by numerical integration of the Schrödinger equation

Tolsma, L.D.; Veltkamp, G.W.

doi:10.1016/0010-4655(86)90112-8

Cited by 8 publications

(5 citation statements)

References 10 publications

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“…The relative motion of three clusters is described in the space of 064308-6 hyperspherical coordinates (ρ, 5 ), and the nuclear wave function J π is decomposed on a basis of hyperspherical harmonics ϒ Kν ( 5 ) [20], J π = Kν ψ J π Kν (ρ)ϒ Kν ( 5 ). Here, ρ, 5 , and K are the hyperradius, hyperangles, and hypermoment, respectively. The index ν denotes all quantum numbers in addition to K, which are needed for a complete identification of the basis.…”

Section: Discussionmentioning

confidence: 99%

“…The index ν denotes all quantum numbers in addition to K, which are needed for a complete identification of the basis. If the Schrödinger equation for the wave function J π is multiplied by hyperspherical harmonics ϒ Kν ( 5 ) from the left and integrated over hyperangles 5 , a system of coupled hyperradial differential equations similar to (1) is obtained. In this system, L i = K i + 3/2 are the generalized orbital angular momenta, where K i is the hypermoment in the ith channel, and the matrix elements V ij (ρ) (containing all intercluster interactions) in the basis of hyperspherical harmonics depend only on the hyperradius ρ.…”

Section: Discussionmentioning

confidence: 99%

“…* ershov@theor.jinr.ru Different methods have been suggested to maintain linear independence, such as a variety of stabilizing transformations during propagation of a solution [1][2][3][4][5]. Usually these transformations are rather awkward and tedious.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modified variable phase method for the solution of coupled radial Schrödinger equations

2011

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A modified variable phase method for the numerical solution of coupled radial Schrödinger equations, which maintains linear independence for different sets of solution vectors, is suggested. The modification involves rearrangement of coupled equations to avoid the usual numerical instabilities associated with components of the wave function in their classically forbidden regions. The modified method is applied to nuclear structure calculations of halo nuclei within the hyperspherical harmonics approach.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Modified variable phase method for the solution of coupled radial Schrödinger equations

2011

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“…For the general Numerov method, Tolsma and Veltkamp [61] have pointed out that an exponentially growing part and an exponentially decreasing part will be produced as R increases through a classically forbidden region, where the local kinetic energy is negative. The former one reduces the linear dependence of the coupled channels solutions and leads to the failure of solving coupled channels equation.…”

Section: Data Availability Statementmentioning

confidence: 99%

Application of the Lagrange-mesh method in continuum-discretized coupled-channel calculations

Chen¹,

Guo²,

Ye³

et al. 2022

J. Phys. G: Nucl. Part. Phys.

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We apply the Lagrange-mesh method to discretize continuum states of weakly bound nuclei for continuum-discretized coupled-channel (CDCC) calculations of three-body breakup reactions. This discretization method is compared with the bin method, which is regarded as the standard continuum discretization method, for the $d$ and $^6$Li induced reactions. An improved Numerov algorithm is used to solve the coupled channels equations, which permits a fast integration of equations and a convenient treatment of the closed channels. A new CDCC model code named \emph{CDCC-R} is developed. In all cases, the combination of the Lagrange-mesh method and the Numerov algorithm shows high efficiency and accuracy for the CDCC calculations of the elastic scattering and breakup reactions. Especially, various numerical and physical aspects are discussed for $^6$Li induced reactions. The coupling effects of the continuum states with high orbital angular momentum and closed channels are discussed. Moderate effects are found on the calculations for elastic scattering and breakup reaction when $F$- and $G$-wave continuum states are included in CDCC model space for $^6$Li induced reactions at the incident energies well above the Coulomb barrier. The closed channel effect is found to be indispensable for $^6$Li breakup reaction calculation when the incident energy is around the Coulomb barrier.

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“…In e.g. [8,9,14,36], stabilizing transformations were applied during propagation to prevent overflow and to maintain the linear independence of the n solution vectors. The drawback with such transformations is that they are expensive and should be applied across the entire integration range when strongly closed channels are included.…”

Section: Invariant Imbeddingmentioning

confidence: 99%

Automatic computation of quantum-mechanical bound states and wavefunctions

Ledoux

Daele

2013

Computer Physics Communications

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We discuss the automatic solution of the multichannel Schrödinger equation. The proposed approach is based on the use of a CP method for which the step size is not restricted by the oscillations in the solution. Moreover, this CP method turns out to form a natural scheme for the integration of the Riccati differential equation which arises when introducing the (inverse) logarithmic derivative. A new Prüfer type mechanism which derives all the required information from the propagation of the inverse of the log-derivative, is introduced. It improves and refines the eigenvalue shooting process and implies that the user may specify the required eigenvalue by its index

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Measuring the accuracy of the solution subspace obtained by numerical integration of the Schrödinger equation

Cited by 8 publications

References 10 publications

Modified variable phase method for the solution of coupled radial Schrödinger equations

Modified variable phase method for the solution of coupled radial Schrödinger equations

Application of the Lagrange-mesh method in continuum-discretized coupled-channel calculations

Automatic computation of quantum-mechanical bound states and wavefunctions

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