非定号扰动磁本征值的计数函数
Counting function of magnetic eigenvalues for non-definite sign perturbations
摘要：
我们考虑扰动算子$H(b,V) := H(b,0) + V$，其中$H(b,0)$是具有非恒定磁场的Pauli的$3$ d哈密顿量，$V$是\textit{a non-definite sign electric potential}关于变量沿磁场指数衰减.我们证明了$H(b,V)$在$H(b,0)$的低基态能量零点附近的共振是其本征值，并且集中在半轴$(-\infty,0)$上。此外，我们建立了新的渐近展开式，上界和下界的数量接近零。
英文摘要：
We consider the perturbed operator $H(b,V) := H(b,0) + V$, where $H(b,0)$ is the $3$d Hamiltonian of Pauli with non-constant magnetic field, and $V$ is \textit{a non-definite sign electric potential} decaying exponentially with respect to the variable along the magnetic field. We prove that the only resonances of $H(b,V)$ near the low ground energy zero of $H(b,0)$ are its eigenvalues and are concentrated in the semi axis $(-\infty,0)$. Further, we establish new asymptotic expansions, upper and lower bounds on their number near zero.
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