Direct numerical solution of the Schrödinger equation for quantum scattering problems

Botero, J.; Shertzer, J.

doi:10.1103/physreva.46.r1155

Cited by 45 publications

(25 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To our knowledge, this work represents the first time the formal scattering theory has successfully been used to directly extract ionization amplitudes. It may be possible to improve the speed of the present method by using a variable-spaced grid, like that used by Botero and Shertzer [9] in their finite-element analysis (this would greatly reduce storage requirements as well). Once we have optimized our code for this simplified model we will proceed to include angular momentum.…”

mentioning

confidence: 99%

Complete Numerical Solution of Electron-Hydrogen Model Collision Problem above the Ionization Threshold

Jones

Stelbovics

2000

Phys. Rev. Lett.

View full text Add to dashboard Cite

Benchmark results are presented for electrons colliding with hydrogen atoms in the S-wave (TemkinPoet) model collision problem, which neglects angular momentum. Complete results (elastic, inelastic, and ionization), accurate to 1%, are obtained by numerically integrating Schrödinger's equation subject to correct asymptotic boundary conditions. This marks the first time direct matching to asymptotic boundary conditions has been shown to yield convergent ionization amplitudes for a Coulomb three-body problem. Results are presented for impact energies of 54.4 and 40.8 eV, where comparison with other theories is available.PACS numbers: 34.80. Dp, 31.15.Fx, 34.10. + x, 34.80.Bm The Temkin-Poet [1,2] model of electron-hydrogen scattering is now widely regarded as an ideal testing ground for the development of general methods intended for the full three-body Coulomb problem. Although only s states are included for both the projectile and the atomic electrons, this model problem still contains most of the features that make the real scattering problem hard to solve. Indeed, even in this simplified model, converged energy distributions for ionization cannot generally be obtained via the close-coupling formalism [3]. Any general method that cannot obtain complete, converged results for this model problem will face similar difficulties when applied to the full electron-hydrogen system. For this reason, we believe it is essential to develop a general numerical method capable of solving the Temkin-Poet model completely before angular momentum is included. Here we report such a method. Complete, precision results for e 2

show abstract

mentioning

confidence: 99%

Complete Numerical Solution of Electron-Hydrogen Model Collision Problem above the Ionization Threshold

Jones

Stelbovics

2000

Phys. Rev. Lett.

View full text Add to dashboard Cite

show abstract

“…Due to this interaction the cross section exhibits also oscillating behavior at small energies. The calculated values were compared to other results [10,12,13]. The relative difference was found to be less than 10 −3 .…”

Section: Numerical Methods and Resultsmentioning

confidence: 88%

Scattering Problem and Resonances for Three-Body Coulomb Quantum Systems: Parallel Calculations

Yarevsky

2016

EPJ Web of Conferences

View full text Add to dashboard Cite

Abstract. An approach to the solution of scattering and resonance problems based on splitting the potential into a finite range part and a long range tail part is proposed. The explicit solution to the Schrödinger equation for the long range tail Hamiltonian is used as an incoming wave. This reformulation of the scattering problem makes it suitable for treatment by the exterior complex scaling. The same technique is used to determine resonances of the system. Calculations are performed with the finite element method which allows efficient parallel computations. The approach is illustrated with calculations of the electron resonant scattering on the hydrogen and the helium ion.

show abstract

“…We also note that other groups have been pursuing somewhat similar lattice approaches for computing scattering phase shifts (26,27), wavepacket scattering from hydrogen (L=O) (28), and a model atom approach (2-dimensional) for autoionization (29,24), a comprehensive critique of which is beyond the scope of this progress report.…”

Section: Fully Corbblated Two-electron Systemsmentioning

confidence: 99%

Time-dependent, lattice approach to atomic collisions

Schultz¹

1996

AIP Conference Proceedings

View full text Add to dashboard Cite

Oak Ridge, Tennessee Recent progress in developing and applying methods of direct numerical solution of atomic collision problems is described. Various forms of the three-body problem are used to illustrate these techniques. Specifically, the process of io&ation in proton-, antiproton-, ranging in computational intensity from collisions'simdated in two spatial dimensions to treatment of the three-dimensional, fully correlated two-electron Schrijdinger equation. These w~amples demonstrate the utility and feasibiity of treating strongly interacting atomic systems throueh the-dwendent. lattice anroaches.

show abstract

Direct numerical solution of the Schrödinger equation for quantum scattering problems

Cited by 45 publications

References 21 publications

Complete Numerical Solution of Electron-Hydrogen Model Collision Problem above the Ionization Threshold

Complete Numerical Solution of Electron-Hydrogen Model Collision Problem above the Ionization Threshold

Scattering Problem and Resonances for Three-Body Coulomb Quantum Systems: Parallel Calculations

Time-dependent, lattice approach to atomic collisions

Contact Info

Product

Resources

About