2000/07/18 by Vladimir Kondratiev, Kondratiev, Vladimir, Mikhail Shubin +1
Computer Science · Mathematics · Physics and Astronomy · #35J10 #81Q10 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math-ph #math.MP #math.SP #msc:35J10 #msc:81Q10
paper · pdf · doi:10.48550/arxiv.math/0007111
43 pages
openalex publication_date 2000/07/18 · arxiv created 2001/07/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide sufficient conditions for the discreteness of spectrum for magnetic Schrödinger operators. They generalize the classical result by K.Friedrichs (1934) and earlier results by J.Avron, I.Herbst and B.Simon (1978), A.Dufresnoy (1983) and A.Iwatsuka (1990) which were obtained in the absence of electric field. Our conditions are formulated as conditions of growth at infinity for some effective potentials. More precise sufficient conditions are formulated by use of the Wiener capacity and extend earlier work by A.M.Molchanov (1953) and V.Kondratiev and M.Shubin (1999) who considered the case of the operator without magnetic field. These conditions become necessary and sufficient in case when there is no magnetic field and the electric potential is semi-bounded below.