Asymptotic behavior of eigenfunctions of the three-particle Schrödinger operator. II. Charged one-dimensional particles

Buslaev, V. S.; Levin, S. B.

doi:10.1090/s1061-0022-2011-01147-1

Cited by 11 publications

(4 citation statements)

References 2 publications

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“…The structure of the presented modification is dictated by a method developed earlier in the works [7], [8], [10], [11].…”

Section: Notations Systemmentioning

confidence: 99%

“…Thus a necessity to develop new methods appeared. One of the methods to describe the asymptotics of the three-dimensional charged quantum particles with repulsive pair potentials scattering problem solution has been developed in the recent years within the framework of the approach based on the analogy of the scattering problem with diffraction problem of the wave on a system of infinite semitransparent "screens" with vicinities (see [7,8] and references in the works). These "screens" represent a geometrical places of points in the configuration space of a many-particle system, in which the particles in pair subsystems coincide.…”

Section: Introductionmentioning

confidence: 99%

“…One of the construction criteria is the discrepancy decrease velocity of the heuristically found Schredinger equation solution. In the work [10] the approach developed in [7,8] for a three-body system was generalized for a system of n particles with possible finite distances in pairs which are all well separated from each other. In this work a uniform in all angle variables in configuration space asymptotics of the n like-charged quantum particles scattering problem is constructed on the level of formal asymptotic decompositions.…”

Section: Introductionmentioning

confidence: 99%

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On the leading term of asymptotics of the $n$ like-charged quantum particles scattering problem solution

Koptelov,

Levin

2013

Preprint

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An ansatz describing in terms of formal asymptotic decompositions a leading term of asymptotics of the n three-dimensional like-charged quantum particles scattering problem solution is suggested. The description of the solution in those asymptotic configurations in which it was known earlier (for example, n = 3), coincides with the previously known constructions [1,4,6,8,10]. It is shown that the Schredinger equation discrepancy for the suggested ansatz decreases faster than the potential uniformly in all angle variables at infinity in configuration space. An assumption is made about the structure of the leading term of the asymptotics of the scattering problem solution related to the n three-dimensional quantum particles interacting by a broad class of slowly decreasing pair potentials.

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“…The structure of the presented modification is dictated by a method developed earlier in the works [7], [8], [10], [11].…”

Section: Notations Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the leading term of asymptotics of the $n$ like-charged quantum particles scattering problem solution

Koptelov,

Levin

2013

Preprint

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“…In [135,138], they described analytically and numerically the solution of the quantum scattering problem for the system of three one-dimensional particles with quickly decaying pair potentials. In [137], they described the leading term of the asymptotics of the scattering problem solution for three one-dimensional charged particles. Finally, in [139], they described the leading term of the asymptotics of the scattering problem solution for three three-dimensional charged particles.…”

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confidence: 99%

Untitled

2014

St. Petersburg Math. J.

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Technology (2000). Buslaev always searched for original analytically rich problems, for which the ways to solve them and the results of investigation were difficult to predict. Like the old masters, he liked to work with formulas, and, for him, the way to general constructions of a theory was through the analysis of nontrivial specific problems. From his point of view, this way of thinking was a distinguishing feature of the St. Petersburg mathematical school. Vladimir Buslaev himself possessed a rare talent for working this way.A professor who had just begun to teach when Buslaev was a third-year student recalls that "Vladimir Buslaev was a brilliant student". He continues: "The work of an educator can lead to a professional deformation: if a teacher thinks that he is much better than the students, he is at risk for developing a 'superiority' complex which, as any other complex, is a bad thing. The third-year student Vladimir Buslaev quickly liquidated my complex. This is how it happened. According to the curriculum, we were discussing 2010 Mathematics Subject Classification. Primary 35-00.

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On the Asymptotic Behavior of Eigenfunctions of the Continuous Spectrum at Infinity in Configuration Space for the System of Three Three-Dimensional Like-Charged Quantum Particles

Levin

2017

J Math Sci

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Asymptotic behavior of eigenfunctions of the three-particle Schrödinger operator. II. Charged one-dimensional particles

Cited by 11 publications

References 2 publications

On the leading term of asymptotics of the $n$ like-charged quantum particles scattering problem solution

On the leading term of asymptotics of the $n$ like-charged quantum particles scattering problem solution

Untitled

On the Asymptotic Behavior of Eigenfunctions of the Continuous Spectrum at Infinity in Configuration Space for the System of Three Three-Dimensional Like-Charged Quantum Particles

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