Abstract
We consider the inverse spectral problem for a singular Sturm-Liouville operator with Coulomb potential. In this paper, we give an asymptotic formula and some properties for this problem by using methods of Trubowitz and Poschel.
Highlights
The Sturm-Liouville equation is a second order linear ordinary differential equation of the form − d dx p ( x ) dy dx + (l λr x)) y x) = 0
The transformation of the general second order equation to canonical form and the asymptotic formulas for the eigenvalues and eigenfunctions was given by Liouville
Properties of spectral characteristic were studied for Sturm-Liouville operators with Coulomb potential, which have discontinuity conditions inside a finite interval
Summary
The Sturm-Liouville equation is a second order linear ordinary differential equation of the form. (2016) Inverse Spectral Theory for a Singular Sturm Liouville Operator with Coulomb Potential. The transformation of the general second order equation to canonical form and the asymptotic formulas for the eigenvalues and eigenfunctions was given by Liouville. − y′′ + 1 y + q ( x) y =λ y, x at the origin In these works, properties of spectral characteristic were studied for Sturm-Liouville operators with Coulomb potential, which have discontinuity conditions inside a finite interval. ∫ ψ 2 dxdydz = 1, R3 where ψ is the wave function, h is Planck’s constant and m is the mass of electron In this equation, if the Fourier transform is applied. If we make the necessary transformation, we can get a Sturm-Liouville equation with Coulomb potential y′′.
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