Quantum scattering via the log derivative version of the Kohn variational principle

Manolopoulos, David E.; Wyatt, Róbert E.

doi:10.1016/0009-2614(88)87322-6

Cited by 227 publications

(86 citation statements)

References 25 publications

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“…The points {x i } and weights {w i } are in turn derived from a Gauss-Lobatto quadrature [38], which is similar to the more familiar Gauss-Legendre quadrature, except that two of the points are constrained to coincide with the interval endpoints. Under the Gauss quadrature rule, the functions are orthonormal and provide a diagonal representation of any local operator…”

Section: B Finite-element/ Discrete Variable Representationmentioning

confidence: 99%

Double photoionization of aligned molecular hydrogen

et al. 2006

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We present converged, completely ab initio calculations of the triple differential cross sections for double photoionization of aligned H2 molecules for a photon energy of 75.0 eV. The method of exterior complex scaling, implemented with both the discrete variable representation and B-splines, is used to solve the Schrödinger equation for a correlated continuum wave function corresponding to a single photon having been absorbed by a correlated initial state. Results for a fixed internuclear distance are compared with recent experiments and show that integration over experimental angular and energy resolutions is necessary to produce good qualitative agreement, but does not eliminate some discrepancies. Limitations of current experimental resolution are shown to sometimes obscure interesting details of the cross section.

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Section: B Finite-element/ Discrete Variable Representationmentioning

confidence: 99%

Double photoionization of aligned molecular hydrogen

et al. 2006

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“…Our DVR basis functions π i (R) are defined by the Gauss-Lobatto quadrature points x i and weights w i [24]. This quadrature approximates integrals of a function g (x) as…”

Section: Methodsmentioning

confidence: 99%

Numerical study of three-body recombination for systems with many bound states

Wang¹,

D'Incao²,

Greene³

2011

Phys. Rev. A

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Three-body recombination processes are treated numerically for a system of three identical bosons. The two-body model potentials utilized support many bound states, a major leap in complexity that produces an intricate structure of sharp nonadiabatic avoided crossings in the three-body hyperradial adiabatic potentials at short distances. This model thus displays the usual difficulties of more realistic systems. To overcome the numerical challenges associated with sharp avoided crossings, the slow variable discretization (SVD) approach is adopted in the region of small hyperradii. At larger hyperradii, where the adiabatic potentials and couplings are smooth, the traditional adiabatic method suffices. Despite the high degree of complexity, recombination into deeply bound states behaves regularly due to the dominance of one decay pathway, resulting from the strong coupling between different recombination channels. Moreover, the usual Wigner threshold law must be modified for excited incident recombination channels.

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“…This was expected since it is wellknown that high-order methods are efficient for the TDSE. These kind of finite elements have also been applied to quantum scattering problems by Manolopoulos and Wyatt [44] as well as Rescigno and McCurdy [49].…”

Section: Finite Element Discretizationmentioning

confidence: 99%

A Time-Space Adaptive Method for the Schrödinger Equation

Kormann

2016

Commun. Comput. Phys.

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Abstract. In this paper, we present a discretization of the time-dependent Schrödinger equation based on a Magnus-Lanczos time integrator and high-order Gauss-Lobatto finite elements in space. A truncated Galerkin orthogonality is used to obtain dualitybased a posteriori error estimates that address the temporal and the spatial error separately. Based on this theory, a space-time adaptive solver for the Schrödinger equation is devised. An efficient matrix-free implementation of the differential operator, suited for spectral elements, is used to enable computations for realistic configurations. We demonstrate the performance of the algorithm for the example of matter-field interaction.

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Quantum scattering via the log derivative version of the Kohn variational principle

Cited by 227 publications

References 25 publications

Double photoionization of aligned molecular hydrogen

Double photoionization of aligned molecular hydrogen

Numerical study of three-body recombination for systems with many bound states

A Time-Space Adaptive Method for the Schrödinger Equation

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