Half-Line non-self-adjoint Schr\"odinger operators with polynomial potentials: Asymptotics of eigenvalues
Shin, Kwang C.
arXiv, 0502522 / Harvested from arXiv
Text on arXiv
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 $\alpha u(0)+\beta u^{\prime}(0)=0$ for some $\alpha, \beta\in\C$ with $|\alpha|+|\beta|\not=0$, 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.
Publié le : 2005-02-24
Classification:  Mathematics - Spectral Theory,  High Energy Physics - Theory,  Mathematical Physics,  Quantum Physics,  34L40,  34L20,  34E05,  34E10 
@article{0502522,
     author = {Shin, Kwang C.},
     title = {Half-Line non-self-adjoint Schr\"odinger operators with polynomial
  potentials: Asymptotics of eigenvalues},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0502522}
}

Shin, Kwang C. Half-Line non-self-adjoint Schr\"odinger operators with polynomial
  potentials: Asymptotics of eigenvalues. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0502522/