Stability of the magnetic Schrödinger operator in a waveguide
نویسنده
چکیده
The spectrum of the Schrödinger operator in a quantum waveguide is known to be unstable in two and three dimensions. Any enlargement of the waveguide produces eigenvalues beneath the continuous spectrum [BGRS]. Also if the waveguide is bent eigenvalues will arise below the continuous spectrum [DE]. In this paper a magnetic field is added into the system. The spectrum of the magnetic Schrödinger operator is proved to be stable under small local deformations and also under small bending of the waveguide. The proof includes a magnetic Hardy-type inequality in the waveguide, which is interesting in its own.
منابع مشابه
Spectral Series of the Schrödinger Operator in a Thin Waveguide with a Periodic Structure. 2. Closed Three-Dimensional Waveguide in a Magnetic Field
Abstract. In the paper, which is the second part of the paper by J. Brüning, S. Dobrokhotov, S. Sekerzh-Zenkovich, T. Tudorovskiy, “Spectral series of the Schrödinger operator in thin waveguides with a periodic structure. 1,” Russ. J. Math. Phys. 13 (4), 401–420 (2006), using the adiabatic approximation, diverse quantum states of the stationary Schrödinger equation for a particle in a thin wave...
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