A second eigenvalue bound for the Dirichlet Schrödinger equation wtih a radially symmetric potential ∗

@inproceedings{Haile2000ASE,
  title={A second eigenvalue bound for the Dirichlet Schr{\"o}dinger equation wtih a radially symmetric potential ∗},
  author={Craig Haile},
  year={2000}
}
  • Craig Haile
  • Published 2000
We study the time-independent Schrödinger equation with radially symmetric potential k|x|, k ≥ 0, k ∈ R, α ≥ 2 on a bounded domain Ω in R, (n ≥ 2) with Dirichlet boundary conditions. In particular, we compare the eigenvalue λ2(Ω) of the operator −∆+ k|x| on Ω with the eigenvalue λ2(S1) of the same operator −∆+ kr α on a ball S1, where S1 has radius such that the first eigenvalues are the same (λ1(Ω) = λ1(S1)). The main result is to show λ2(Ω) ≤ λ2(S1). We also give an extension of the main… CONTINUE READING