Sharp Spectral Asymptotics for four-dimensional Schroedinger operator with a strong magnetic field. II

arXivmath/0612252MaRDI QIDQ6478408

Victor Ivrii

Publication date: 10 December 2006

Abstract: I consider 4-dimensional Schr"odinger operator with the generic non-degenerating magnetic field and for a generic potential I derive spectral asymptotics with the remainder estimate $O(m{u}^{-1}{h}^{-3})$ and the principal part $asymp{h}^{-4}$ where $hll1$ is Planck constant and $mugg1$ is the intensity of the magnetic field. For general potentials remainder estimate $O(m{u}^{-1}{h}^{-3}+m{u}^2{h}^{-2})$ is achieved.

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20)

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