Half-Line non-self-adjoint Schrödinger operators with polynomial potentials: Asymptotics of eigenvalues
| dc.creator | Shin, Kwang C. | |
| dc.date | 2005-02-24 | |
| dc.date.accessioned | 2026-07-07T05:17:27Z | |
| dc.date.available | 2026-07-07T05:17:27Z | |
| dc.description | For integers $m\geq 3$, we study the non-self-adjoint eigenvalue problems $-u^{\prime\prime}(x)+(x^m+P(x))u(x)=E u(x)$, $0\leq x<+\infty$, with the boundary conditions $u(+\infty)=0$ and $αu(0)+βu^{\prime}(0)=0$ for some $α, β\in\C$ with $|α|+|β|\not=0$, where $P(x)=a_1 x^{m-1}+a_2 x^{m-2}+...+a_{m-1} x$ is a polynomial. We provide asymptotic expansions of the eigenvalue counting function and the eigenvalues $E_{n}$. Then we apply these to the inverse spectral problem, reconstructing some coefficients of polynomial potentials from asymptotic expansions of the eigenvalues. | |
| dc.description | 15 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0502522 | |
| dc.identifier | http://arxiv.org/abs/math/0502522 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74312 | |
| dc.subject | Spectral Theory | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | Quantum Physics | |
| dc.subject | 34L40; 34L20; 34E05; 34E10 | |
| dc.title | Half-Line non-self-adjoint Schrödinger operators with polynomial potentials: Asymptotics of eigenvalues | |
| dc.type | text |