從1915年Jeans提出物質穩定性的問題到現在,穩定性一直是物理學家所關心且探討的主題.來自該問題所引發的動機,我們透過探討類氫原子在角動量量子數l=0 的行為,重新思考原子的穩定性問題.利用拉普拉斯轉換解二階微分方程的方法,我們得到類氫原子l=0 時在電子接近原子核時的精確行為,並進而發現崩潰態的存在.而當我們在拋物線座標探討相同問題時,我們得到造成崩潰態存在的主要原因是來自類氫原子在l=0 時波函數具有球狀對稱的特性.除此之外,我們使用分波法理論性地探討l=0 的分波被常數排斥性位勢散射的現象,並得到入射l=0 的波遵守海更士原理的條件是該位勢必須具有某些特定的寬度.

Motivated by the stability question mentioned by Jeans, we investigate the behavior of hydrogen-like atom in l=0 state since it involves thestability of an atom. The existence of collapse state and the exact behavior of the wave function for l=0 in hydrogen-like atom near the nucleus are obtained by using the Laplace transformation. By dealing with the same question in parabolic coordinates, we find the cause ofcollapse is due entirely to the perfect spherical symmetry in the l=0state for hydrogen-like atom. In addition, we theoretically discuss the phenomenon of l=0 partial wave of particle scattered by a constant repulsive potential. It gives the condition for the incident partial wave to obey the Huygens' principle.