电势递减磁薛定谔算子的准经典与非经典谱渐近性
Quasi-classical versus non-classical spectral asymptotics for magnetic Schroedinger operators with decreasing electric potentials
摘要：
我们考虑L^2（R^2）或L^2（R^3）上的Schroedinger算子H，其中具有恒定磁场和电势V，它通常在无穷远处指数快速衰减或具有紧支撑。研究了H的离散谱在其本质谱边界点附近的渐近行为。如果V的衰减是高斯或更快，这种行为是非经典的，因为它不是由V允许幂类衰减的情况下已知的准经典公式描述的。
英文摘要：
We consider the Schroedinger operator H on L^2(R^2) or L^2(R^3) with constant magnetic field and electric potential V which typically decays at infinity exponentially fast or has a compact support. We investigate the asymptotic behaviour of the discrete spectrum of H near the boundary points of its essential spectrum. If the decay of V is Gaussian or faster, this behaviour is non-classical in the sense that it is not described by the quasi-classical formulas known for the case where V admits a power-like decay.
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