中心势中束缚态存在的充要条件
Necessary and sufficient conditions for existence of bound states in a central potential
摘要：
在非相对论性量子力学的背景下，利用Birman-Schwinger方法，我们得到了至少存在一个束缚态的一系列必要条件.这些条件产生一个单调系列的下限的“临界”值的强度的潜力（其中第一个绑定状态出现），收敛到确切的临界强度。我们还得到了中心单调势中存在束缚态的一个充分条件，该条件给出了中心单调势临界强度的一个上限。
英文摘要：
We obtain, using the Birman-Schwinger method, a series of necessary conditions for the existence of at least one bound state applicable to arbitrary central potentials in the context of nonrelativistic quantum mechanics. These conditions yield a monotonic series of lower limits on the "critical" value of the strength of the potential (for which a first bound state appears) which converges to the exact critical strength. We also obtain a sufficient condition for the existence of bound states in a central monotonic potential which yield an upper limit on the critical strength of the potential.
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