论文标题
一维氢原子的结合溶液
The bound-state solutions of the one-dimensional hydrogen atom
论文作者
论文摘要
一维氢原子是一个有趣的量子力学问题，表现出几种持续辩论的特性。特别是，关于是否存在偶数解决方案，尤其是基态是否是具有无限的负能量的偶数状态，存在差异。我们研究了该系统的“正规化”版本，该版本的电势是原点附近的常数，我们讨论了这种正则化的一维氢原子的偶数和奇数溶液。我们展示了偶数状态以外的状态以外的态度如何融合到相同的功能形式，并以$ x> 0 $变性，随着截止量接近零，奇数> 0 $。这与从分析（即没有正则化）一维库仑电位的分析得出的结论不同，那里的频谱中没有均匀溶液。
The one-dimensional hydrogen atom is an intriguing quantum mechanics problem that exhibits several properties which have been continually debated. In particular, there has been variance as to whether or not even-parity solutions exist, and specifically whether or not the ground state is an even-parity state with infinite negative energy. We study a "regularized" version of this system, where the potential is a constant in the vicinity of the origin, and we discuss the even- and odd-parity solutions for this regularized one-dimensional hydrogen atom. We show how the even-parity states, with the exception of the ground state, converge to the same functional form and become degenerate for $x > 0$ with the odd-parity solutions as the cutoff approaches zero. This differs with conclusions derived from analysis of the singular (i.e., without regularization) one-dimensional Coulomb potential, where even-parity solutions are absent from the spectrum.
