The inverse problem for perturbed harmonic oscillator on the half-line
Chelkak, Dmitry ; Korotyaev, Evgeny
arXiv, 0508056 / Harvested from arXiv
Text on arXiv
We consider the perturbed harmonic oscillator $T_D\psi=-\psi''+x^2\psi+q(x)\psi$, $\psi(0)=0$ 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 $\psi'(0)=b \psi(0)$, $b\in R$.
Publié le : 2005-08-29
Classification:  Mathematical Physics,  Mathematics - Spectral Theory 
@article{0508056,
     author = {Chelkak, Dmitry and Korotyaev, Evgeny},
     title = {The inverse problem for perturbed harmonic oscillator on the half-line},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0508056}
}

Chelkak, Dmitry; Korotyaev, Evgeny. The inverse problem for perturbed harmonic oscillator on the half-line. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0508056/