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Point perturbation-invariant solutions of the Schrödinger equation with a magnetic field. (English. Russian original) Zbl 0898.35081
Math. Notes 60, No. 5, 575-580 (1996); translation from Mat. Zametki 60, No. 5, 768-773 (1996).
Let $$\Omega_\Lambda$$ be a unit cell of the lattice $$\Lambda$$, which is a parallelogram of the form $$\{x\in \mathbb{R}^2: x=t_1\vec a_1+ t_2\vec a_2$$, $$0\leq t_1$$, $$t_2<1\}$$ spanning a pair of basis vectors of the lattice $$(\vec a_1, \vec a_2)$$. We denote the area of $$\Omega_\Lambda$$ by $$S_\Lambda$$, the number of elements in $$\Omega_\Lambda \cap \Gamma$$ by $$k$$, and the number of quanta of the magnetic flux across a unit cell of $$\Lambda$$ by $$\eta$$, $$\eta= S_\Lambda \xi$$.
The aim of this note is to prove that for any $$k$$ and for any level $$\varepsilon_l$$, the validity of the inequality $$|\eta |>k$$ is a sufficient condition for the existence of Landau-Ando states.
##### MSC:
 35Q40 PDEs in connection with quantum mechanics 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis 35Q60 PDEs in connection with optics and electromagnetic theory
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