A transmutation operator method for solving the inverse quantum scattering problem *

DOI10.1088/1361-6420/abbf8fzbMath1471.34162arXiv2007.13039OpenAlexW3044648946MaRDI QIDQ5139330

Sergii M. Torba, Vladislav V. Kravchenko, Elina Leonidovna Shishkina

Publication date: 8 December 2020

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.13039

zbMATH Keywords

Bubnov-Galerkin methodNeumann series of Bessel functionstransmutation operatorperturbed Bessel equationGel'fand-Levitan equationinverse quantum scattering problemhigher waves

Mathematics Subject Classification ID

Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Inverse problems involving ordinary differential equations (34A55) Scattering theory, inverse scattering involving ordinary differential operators (34L25) Numerical solution of inverse problems involving ordinary differential equations (65L09)

Related Items (5)

Inverse nodal problems for singular problems in the half-line ⋮ Realization of the inverse scattering transform method for the Korteweg–de Vries equation ⋮ Spectrum completion and inverse Sturm–Liouville problems ⋮ Professor Vladislav V. Kravchenko: a mathematician and a friend ⋮ Reconstruction techniques for complex potentials

Cites Work

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• Dispersion estimates for spherical Schrödinger equations
• Expansion in series of Bessel functions and transmutations for perturbed Bessel operators
• Bargmann's inequalities in spaces of arbitrary dimension
• On a series representation for integral kernels of transmutation operators for perturbed Bessel equations
• On numerical evaluation of integrals involving oscillatory Bessel and Hankel functions
• Transmutations, singular and fractional differential equations with applications to mathematical physics
• On a method for solving the inverse Sturm-Liouville problem
• Transformation operators for spherical Schrödinger operators
• Spectral asymptotics for perturbed spherical Schrödinger operators and applications to quantum scattering
• Inverse eigenvalue problems for perturbed spherical Schrödinger operators
• On a method for solving the inverse scattering problem on the line
• Dispersion estimates for spherical Schrödinger equations with critical angular momentum
• Direct and Inverse Sturm-Liouville Problems
• The transmutation operator method for efficient solution of the inverse Sturm‐Liouville problem on a half‐line
• On the Coulomb and Hulthen Potentials

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