Energy spectrum design and potential function engineering

DOI10.1134/S0040577923070097arXiv2211.09329OpenAlexW4384271160MaRDI QIDQ6167622

T. J. Taiwo, A. D. Alhaidari

Publication date: 7 August 2023

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2211.09329

zbMATH Keywords

wavefunctionorthogonal polynomialsscattering phase shiftcontinuous dual Hahn polynomialrecursion relationenergy spectrum designpotential function engineering

Mathematics Subject Classification ID

Inverse scattering problems in quantum theory (81U40) Applications of hypergeometric functions (33C90)

Cites Work

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• Inversion of a tridiagonal Jacobi matrix
• Representation of the quantum mechanical wavefunction by orthogonal polynomials in the energy and physical parameters
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• Non-uniqueness in the one-dimensional inverse scattering problem
• SO(2,1) Lie algebra, the Jacobi matrix and the scattering states of the Morse oscillator
• Scattering Theory and Polynomials Orthogonal on the Real Line
• A Relation between the Coefficients in the Recurrence Formula and the Spectral Function for Orthogonal Polynomials
• A Review on the Inverse of Symmetric Tridiagonal and Block Tridiagonal Matrices
• Reconstructing the Potential Function in a Formulation of Quantum Mechanics Based on Orthogonal Polynomials
• Orthogonal polynomials from the viewpoint of scattering theory
• Confined systems with a linear energy spectrum
• Quantum mechanics without potential function
• The uniqueness of the solution of the inverse problem in potential theory

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