The inverse problem for perturbed harmonic oscillator on the half-line
| dc.creator | Chelkak, Dmitry | |
| dc.creator | Korotyaev, Evgeny | |
| dc.date | 2005-08-29 | |
| dc.date.accessioned | 2026-07-07T04:32:18Z | |
| dc.date.available | 2026-07-07T04:32:18Z | |
| dc.description | We consider the perturbed harmonic oscillator $T_Dψ=-ψ''+x^2ψ+q(x)ψ$, $ψ(0)=0$ in $L^2(R_+)$, where $q\in H_+=\{q', xq\in L^2(R_+)\}$ is a real-valued potential. We prove that the mapping $q\mapsto{\rm spectral data}={\rm \{eigenvalues of\}T_D{\rm \}}\oplus{\rm \{norming constants\}}$ is one-to-one and onto. The complete characterization of the set of spectral data which corresponds to $q\in H_+$ is given. Moreover, we solve the similar inverse problem for the family of boundary conditions $ψ'(0)=b ψ(0)$, $b\in R$. | |
| dc.identifier | https://arxiv.org/abs/math-ph/0508056 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0508056 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58141 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Spectral Theory | |
| dc.title | The inverse problem for perturbed harmonic oscillator on the half-line | |
| dc.type | text |