具有紧化额外维数和高斯势空间中的氢原子
Hydrogen atom in space with a compactified extra dimension and potential defined by Gauss' law
摘要：
研究了一个额外的空间维度对具有高斯定律定义的势的非相对论性氢原子的稳定性和能谱的影响，即与$1/|x|^2$成正比。附加的空间维度被认为是无限的或卷曲在半径为$R$的圆中。在这两种情况下，能谱是有界的，从下面小于相同的临界值和无界的电荷从下面。紧化的结果是，出现负能量本征态：如果$R$小于玻尔半径的四分之一，则相应的哈密顿量具有无限多的束缚态，其最小能量至少延伸到氢原子的基态。
英文摘要：
We investigate the consequences of one extra spatial dimension for the stability and energy spectrum of the non-relativistic hydrogen atom with a potential defined by Gauss' law, i.e. proportional to $1/|x|^2$. The additional spatial dimension is considered to be either infinite or curled-up in a circle of radius $R$. In both cases, the energy spectrum is bounded from below for charges smaller than the same critical value and unbounded from below otherwise. As a consequence of compactification, negative energy eigenstates appear: if $R$ is smaller than a quarter of the Bohr radius, the corresponding Hamiltonian possesses an infinite number of bound states with minimal energy extending at least to the ground state of the hydrogen atom.
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