Schrödinger type eigenvalue problems with polynomial potentials: Asymptotics of eigenvalues

Kwang C. Shin

For integers $m\ge 3$ and $1\le \ell \le m-1$, we study the eigenvalue problem $-u^{\prime \prime }(z)+[(-1{)}^{\ell }(iz{)}^m-P(iz)]u(z)=\lambda u(z)$ with the boundary conditions that $u(z)$…