论文标题
1D量子力学中能量依赖性点状相互作用的正则化
Regularization of energy-dependent pointlike interactions in 1D quantum mechanics
论文作者
论文摘要
我们在1D量子力学中构建了一个遗传电位的家族，该家族在零范围的限制中收敛到$δ$相互作用，并与能量依赖性耦合相互作用。它脱离了1D中标准的四参数类似点状相互作用的家族。这样的分类是通过要求尖端的互动作为隐居者进行的。但是我们表明，尽管当电位范围是有限的范围时，我们的哈密顿量是标准内部产品的隐居，但在零范围极限下，它成为了不同内部产品的隐居。该内部产物归因于粒子精确位于电势位置的有限概率（而不是概率密度）。然后，这种类似点的相互作用可用于构建具有有限支撑的电势，并具有依赖能量的耦合。
We construct a family of hermitian potentials in 1D quantum mechanics that converges in the zero-range limit to a $δ$ interaction with an energy-dependent coupling. It falls out of the standard four-parameter family of pointlike interactions in 1D. Such classification was made by requiring the pointlike interaction to be hermitian. But we show that although our Hamiltonian is hermitian for the standard inner product when the range of the potential is finite, it becomes hermitian for a different inner product in the zero-range limit. This inner product attributes a finite probability (and not probability density) for the particle to be exactly located at the position of the potential. Such pointlike interactions can then be used to construct potentials with a finite support with an energy-dependent coupling.
