Asymptotic Behaviors of the Eigenvalues of Schrödinger Operator with Critical Potential

Abstract

We study the asymptotic behaviors of the discrete eigenvalue of Schrödinger operator P(λ)=P0+λV with P0=-Δ+qθ/r2. We obtain the leading terms of discrete eigenvalues of P(λ) when the eigenvalues tend to 0. In particular, we obtain the asymptotic behaviors of eigenvalues when (P0−α)−1 has singularity at α=0.