一维四参数点相互作用多体系统
Many-body system with a four-parameter family of point interactions in one dimension
摘要：
我们考虑一维点相互作用的四参数族。这个族是通常的$δ$ -函数势的推广。我们研究了一个系统，由许多粒子的质量相等，相互作用成对通过这样一个广义点相互作用。我们遵循McGuire谁获得了系统的精确解时的相互作用是$δ$功能的潜力。我们发现确切的束缚态与四参数家庭。然而，对于散射问题，我们还没有那么成功。这是因为，正如我们所指出的，没有衍射的条件是至关重要的，在麦圭尔的方法是不满足的，除非当四参数家庭基本上是减少到$δ$ -功能的潜力。
英文摘要：
We consider a four-parameter family of point interactions in one dimension. This family is a generalization of the usual $δ$-function potential. We examine a system consisting of many particles of equal masses that are interacting pairwise through such a generalized point interaction. We follow McGuire who obtained exact solutions for the system when the interaction is the $δ$-function potential. We find exact bound states with the four-parameter family. For the scattering problem, however, we have not been so successful. This is because, as we point out, the condition of no diffraction that is crucial in McGuire's method is not satisfied except when the four-parameter family is essentially reduced to the $δ$-function potential.
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