# On a class of Schrödinger operators exhibiting spectral transition

### Diana Barseghyan

University of Ostrava, Czech Republic### Olga Rossi

University of Ostrava, Czech Republic

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## Abstract

We show that the operator for $\lambda<\frac{\pi^2}{4}$ is bounded from below and has purely discrete spectrum, while for $\lambda>\frac{\pi^2}{4}$ its spectrum contains the real line. In the critical case $\lambda=\frac{\pi^2}{4}$ we prove that the spectrum coincides with the half line $[0, \infty)$.