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- W172372709 abstract "In this chapter we analyze two- and three-dimensional Schrödinger operators with strong magnetic field; now we have not only a small parameter h but a large parameter μ (a coupling constant with the magnetic field or simply a magnetic parameter); moreover, a natural condition μ ≤ h −1 arises. In section 6.1, which has a preliminary character, we obtain a formula for e(x,x,τ), for operators in ℝd with constant g jk,V and F jk (which is the tensor intensity of the magnetic field) and we also prove some preliminary assertions. In section 6.2 we obtain microlocal canonical forms for d = 2, 3 which are the basis for the advanced analysis. In section 6.3 we derive (quasi-)Weylian and related formulas for d = 2,3 in the case of a weak magnetic field (μ ≤ h δ−1) and in section 6.4 we derive non-Weylian formulas in the case of a strong magnetic field (μ ≥ h δ−1); these formulas permit us to justify the (quasi-)Weylian formulas under weaker restrictions than those of section 6.3.KeywordsIntegral FormulaTotal ContributionExtra TermPrincipal SymbolMagnetic LineThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves." @default.
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- W172372709 date "1998-01-01" @default.
- W172372709 modified "2023-09-27" @default.
- W172372709 title "Local Spectral Asymptotics for the Schrödinger Operator with Strong Magnetic Field" @default.
- W172372709 doi "https://doi.org/10.1007/978-3-662-12496-3_7" @default.
- W172372709 hasPublicationYear "1998" @default.
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