从散射振幅得到的二体波函数和复合性。I.原理图模型的常规属性
Two-body wave functions and compositeness from scattering amplitudes. I. General properties with schematic models
摘要：
对于量子力学中的一般两体束缚态，无论是稳定的还是衰减的，我们建立了一种从组成两粒子的散射振幅中提取其动量空间中的两体波函数的方法.为此，我们首先证明了束缚态的两体波函数对应于离壳层散射振幅在束缚态极点处的留数。然后，我们检查我们的计划，以提取两体波函数的散射振幅在几个示意性的模型。结果表明，对于能量无关的相互作用，Lippmann-Schwinger方程的两体波函数与薛定谔方程的两体波函数是一致的.特别感兴趣的是，从散射振幅的两体波函数自动缩放;的规范的两体波函数，我们称之为复合，是一个能量无关的相互作用的统一，而复合偏离一个能量相关的相互作用，这可以解释为实现丢失的通道的贡献。我们还讨论了两体波函数的一般性质和束缚态的复合性。
英文摘要：
For a general two-body bound state in quantum mechanics, both in the stable and decaying cases, we establish a way to extract its two-body wave function in momentum space from the scattering amplitude of the constituent two particles. For this purpose, we first show that the two-body wave function of the bound state corresponds to the residue of the off-shell scattering amplitude at the bound state pole. Then, we examine our scheme to extract the two-body wave function from the scattering amplitude in several schematic models. As a result, the two-body wave functions from the Lippmann--Schwinger equation coincides with that from the Schrödinger equation for an energy-independent interaction. Of special interest is that the two-body wave function from the scattering amplitude is automatically scaled; the norm of the two-body wave function, to which we refer as the compositeness, is unity for an energy-independent interaction, while the compositeness deviates from unity for an energy-dependent interaction, which can be interpreted to implement missing channel contributions. We also discuss general properties of the two-body wave function and compositeness for bound states in the schematic models.
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