The inverse problem for perturbed harmonic oscillator on the half-line

2005/08/29 by Dmitry Chelkak, Chelkak, Dmitry, Evgeny Korotyaev +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math-ph #math.MP #math.SP

paper · pdf · doi:10.48550/arxiv.math-ph/0508056

arxiv created 2005/08/29 · openalex publication_date 2005/08/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the perturbed harmonic oscillator T_Dψ=-ψ''+x²ψ+q(x)ψ, ψ(0)=0 in L²(R₊), where q∈ H₊=\q', xq∈ L²(R₊)\ is a real-valued potential. We prove that the mapping q↦\rm spectral data=\rm \eigenvalues of\T_D\rm \⊕\rm \norming constants\ is one-to-one and onto. The complete characterization of the set of spectral data which corresponds to q∈ H₊ is given. Moreover, we solve the similar inverse problem for the family of boundary conditions ψ'(0)=b ψ(0), b∈ R.

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