标题： 一维薛定谔算子点相互作用的物理解释 显示英文标题

标题： Physical interpretation of point-like interactions of one-dimensional Schrödinger operator

摘要： 我们考虑无自旋粒子的一维薛定谔算子的自伴扩张的非平凡边界条件的物理解释。 尽管这个问题具有模型性和相当抽象的特性，但由于其在一维纳米结构中的应用，值得进行研究。 主要结果是对一种特殊的自伴扩张的物理解释，该扩张具有概率密度和波函数导数的不连续性。 我们表明，这种情况与之前考虑的其他三种情况有很大不同，并且在甘娜拉等人的工作（《物理杂志A：数学和理论》42, 465207 (2009)）的意义上对应于质量跳跃以及量子化磁通量的共存。 可以由这种边界条件建模的现实物理系统是两个具有不同基本激发有效质量的超导体之间的约瑟夫森结中的局域量子化通量。 显示英文摘要

摘要： We consider physical interpretations of non-trivial boundary conditions of self-adjoint extensions for one-dimensional Schr\"odinger operator of free spinless particle. Despite its model and rather abstract character this question is worth of investigation due to application for one-dimensional nanostructures. The main result is the physical interpretation of peculiar self-adjoint extension with discontinuity of both the probability density and the derivative of the wave function. We show that this case differs very much from other three which were considered before and corresponds to the presence of mass-jump in a sense of works of Ganella et. al., (Journal of Physics A: Mathematical and Theoretical 42, 465207 (2009)) along with the quantized magnetic flux. Real physical system which can be modeled by such boundary conditions is the localized quantazied flux in the Josephson junction of two superconductors with different effective masses of the elementary excitations.