O. Safronov

activity

20092022

most citedEstimates for eigenvalues of the Schrödinger operator with a complex potential

56 citations · 65 across the 6 of their papers we have counts for

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5 papers · 1 filter

math-ph2022

The rate of accumulation of negative eigenvalues to zero and the absolutely continuous spectrum

Oleg Safronov

For a bounded real-valued function $V$ on $R^{d}$ , we consider two Schrödinger operators $H_{+} = - Δ + V$ and $H_{-} = - Δ - V$ . We prove that if the negative spectra $H_{+}$ and $H_{-}$ are d…

math-ph2021

Absolutely continuous and pure point spectra of discrete operators with sparse potentials

S. Molchanov, O. Safronov, B. Vainberg

We consider the discrete Schrödinger operator $H = - Δ + V$ with a sparse potential $V$ and find conditions guaranteeing either existence of wave operators for the pair $H$ and $H_{0} = - Δ$ …

math-ph2011★ 2 cited

Absolutely continuous spectrum of a typical Schrödinger operator with a slowly decaying potential

Oleg Safronov

We consider a family of multi-dimensional Schrödinger operators $- Δ + t V$ with a real $t$ . The potential $V$ in our model decays at infinity in a special way, so that it satisfies a…

math-ph2009

On a sum rule for Schrödinger operators with complex potentials

Oleg Safronov

We study the distribution of eigenvalues of the one-dimensional Schrödinger operator with a complex valued potential $V$ . We prove that if $∣ V ∣$ decays faster than the Coulomb pote…

math-ph2009★ 56 cited

Estimates for eigenvalues of the Schrödinger operator with a complex potential

Oleg Safronov

We study the distribution of eigenvalues of the Schrödinger operator with a complex valued potential $V$ . We prove that if $∣ V ∣$ decays faster than the Coulomb potential, then all…