论文标题
波功能中的非分析性和奇异性的存在以及看不见的三角电势的作用
The presence of non-analyticities and singularities in the wavefunction and the role of invisible delta potentials
论文作者
论文摘要
本文研究了参考文献中提出的建议。 [EPL，115（2016）60001]对于无限球形井模型中粒子的解决方案，如果是正方形的融合，则是一个物理上有效的解决方案，即使在奇异性的确切位置没有潜在的物理原因的确切位置，因此，差异必须是由距离隔开的距离，这是一个非局部现象。在这项工作中，我们更仔细地研究了这一说法。通过识别可发射的正方形集成溶液的正确微分方程并以Schroedinger方程的形式重写，我们推断出发散的波函数将由电位V（R）= -R Delta（R）引起，这是一种有吸引力的Delta电位。由于其奇特的形式以及它导致势能<v> = - 无穷大的事实，势V（r）和与之相关的发散波函数在物理上没有意义。
This article examines the suggestion made in Ref. [EPL, 115 (2016) 60001] that a solution to a particle in an infinite spherical well model, if it is square-integrable, is a physically valid solution, even if at the precise location of the singularity there is no underlying physical cause, therefore, the divergence would have to be a nonlocal phenomenon caused by confining walls at a distance. In this work we examine this claim more carefully. By identifying the correct differential equation for a divergent square-integrable solution and rewriting it in the form of the Schroedinger equation, we infer that the divergent wavefunction would be caused by the potential V(r)=-r delta(r), which is a kind of attractive delta potential. Because of its peculiar form and the fact that it leads to a divergent potential energy <V> = - infinity, the potential V(r) and the divergent wavefunction associated with it are not physically meaningful.
