Evgeny Korotyaev

most citedSchrödinger operator with a junction of two 1-dimensional periodic potentials

19 citations · 28 across the 5 of their papers we have counts for

collaborators

5 papers

math-ph2005★ 3 cited

The inverse problem for perturbed harmonic oscillator on the half-line

Dmitry Chelkak, Evgeny Korotyaev

We consider the perturbed harmonic oscillator $T_{D} ψ = - ψ^{''} + x^{2} ψ + q (x) ψ$ , $ψ (0) = 0$ in $L^{2} (R_{+})$ , where $q \in H_{+} = {q^{'}, x q \in L^{2} (R_{+})}$ is a real-valued potential. We prove that the…

math.SP2005

The Lyapunov function for Schrödinger operators with a periodic 2x2 matrix potential

Andrei Badanin, Jochen Brüning, Evgeny Korotyaev

We consider the Schrödinger operator on the real line with a 2x2 matrix valued 1-periodic potential. The spectrum of this operator is absolutely continuous and consists of interval…

math.SP2005★ 6 cited

Spectral asymptotics for periodic fourth order operators

Andrei Badanin, Evgeny Korotyaev

We consider the operator $d^{4} d t^{4} + V$ on the real line with a real periodic potential $V$ . The spectrum of this operator is absolutely continuous and consists of intervals separat…

math.SP2005★ 19 cited

Schrödinger operator with a junction of two 1-dimensional periodic potentials

Evgeny Korotyaev

The spectral properties of the Schrödinger operator $T_{t} y = - y^{''} + q_{t} y$ in $L^{2} (R)$ are studied, with a potential $q_{t} (x) = p_{1} (x), x < 0,$ and $q_{t} (x) = p (x + t), x > 0,$ where $p_{1}, p$ ar…

math-ph2003

Spectral asymptotics of harmonic oscillator perturbed by bounded potential

M. Klein, E. Korotyaev, A. Pokrovski

Consider the operator $T = - d^{2} d x^{2} + x^{2} + q (x)$ in $L^{2} (R)$ , where real functions $q$ , $q^{'}$ and $\int_{0}^{x} q (s) d s$ are bounded. In particular, $q$ is periodic or almost perio…