论文标题
Beta对具有增量潜力的Schrodinger操作员至关重要
Beta Critical for the Schrodinger Operator with Delta Potential
论文作者
论文摘要
对于一个尺寸的schrödinger操作员，在迪利奇边界条件下，我们表明$β_{cr} $对于neumann和robin边界条件的情况是$ v（x）=-βδ（x-a）的势能，零是正，零是$β\ geq 0，$β$β$β。电势以Dirichlet边界条件向边界移动。我们还表明，$β_{Cr}> 0 $和$β\ in（0，\ frac {1} {2}）$考虑了dirichlet问题，在圆圈中具有圆形潜力的dirichlet问题。
For the one dimensional Schrödinger operator in the case of Dirichlet boundary condition, we show that $β_{cr}$ is positive and zero for the case of Neumann and Robin boundary condition considering the potential energy of the form $V(x)=-βδ(x-a)$ where, $β\geq 0, \ a > 0.$ We prove that the $β_{cr}$ goes to infinity when the delta potential moves towards the boundary in dimension one with Dirichlet boundary condition. We also show that the $β_{cr}>0$ and $β\in (0,\frac{1}{2})$ considering Dirichlet problem with delta potential on the circle in dimension two.
