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

Dmitry Chelkak, Evgeny Korotyaev

We consider the perturbed harmonic oscillator $T_D\psi =-{\psi }^{\prime \prime }+x^2\psi +q(x)\psi$, $\psi (0)=0$ in $L^2(R_{+})$, where $q\in H_{+}=\{q^{\prime },xq\in L^2(R_{+})\}$ is a real-valued potential. We prove that the…