Asymptotic Behaviors of the Eigenvalues of Schrödinger Operator with Critical Potential

Abstract EN

We study the asymptotic behaviors of the discrete eigenvalue of Schrödinger operator P ( λ ) = P 0 + λ V with P 0 = - Δ + q θ / r 2 .

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 ( P 0 − α ) − 1 has singularity at α = 0 .