从共振态或虚态微扰生成束缚态的可行性
Feasibility of perturbative generation of bound-states from resonances or virtual states
AI总结：
本文研究一阶微扰理论能否从共振态或虚态生成束缚态，发现虽可得到负能量态，但在定态薛定谔方程和厄米哈密顿量框架下无法形成类似非微扰处理的束缚态结构。
摘要：
我研究了是否可能通过一阶微扰理论从共振态或虚态生成束缚态。利用无π有效场论中出现的接触型势，我证明在存在领头阶共振态或虚态的情况下，通过将次领头阶相互作用与领头阶波函数夹积，可以获得负能量态。然而，至少在定态薛定谔方程和厄米哈密顿量的框架下，无法创建与非微扰处理形成的结构相似的束缚态。
英文摘要：
I investigate whether it is possible to generate bound-states from resonances or virtual states through first-order perturbation theory. Using contact-type potentials as those appeared in pionless effective field theory, I show that it is possible to obtain negative-energy states by sandwiching a next-to-leading order (NLO) interaction with the leading-order (LO) wavefunctions, under the presence of LO resonances or virtual states. However, at least under the framework of time-independent Schrödinger equation and Hermitian Hamiltonian, there is an inability to create bound-states with structure similar to those formed by the non-perturbative treatments.
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