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首页> 外文期刊>The journal of physical chemistry, A. Molecules, spectroscopy, kinetics, environment, & general theory >Feshbach Resonances: The Branching of Quantum Mechanics into Hermitian and Non-Hermitian Formalisms
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Feshbach Resonances: The Branching of Quantum Mechanics into Hermitian and Non-Hermitian Formalisms

机译：菲什巴赫共振：量子力学分为埃尔米特形式主义和非埃尔米特形式主义

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摘要

As has been shown long time ago by Feshbach, the exact energy spectrum of the full problem can be obtained by solving two different self-energy problems. In spite of the fact that the two effective Hamiltonians are derived in very similar ways in one case, the exact energy spectrum of the full problem can be either real or complex (depending on the boundary conditions), whereas the exact energy spectrum associated with the second effective Hamiltonian has to be complex (excluding bound states in the continuum). The focus of this paper is on the fact that in both cases the complex eigenvalues result from the same requirement of an out_going boundary condition. The branching of quantum mechanics to standard (Hermitian) formalism and non-Hermitian formalism is associated with the decision to express the exact energy spectrum with one of the two possible self-consistent like problems where the use of the Green operator imposes an outgoing boundary condition on the solutions of the time-independent Schr_dinger equation. Our analysis is made for the case where an ABC molecule has sufficient energy to dissociate to A + BC but not to A + B + C and not to AB + C or to AC + B.
机译：正如费什巴赫（Feshbach）很久以前所表明的那样，可以通过解决两个不同的自能量问题来获得整个问题的精确能谱。尽管在一个情况下两个有效的哈密顿量是通过非常相似的方式得出的，但整个问题的精确能谱可以是实数或复杂的（取决于边界条件），而与能量相关的精确能谱第二个有效哈密顿量必须是复杂的（不包括连续体中的束缚态）。本文的重点是这样一个事实，在两种情况下，复杂特征值都是由向外边界条件的相同要求导致的。量子力学分支到标准（Hermitian）形式主义和非Hermitian形式主义与决定表达精确的能谱以及两个可能的自洽性问题之一的决定有关，其中使用格林算子会施加外向边界条件与时间无关的Schr_dinger方程的解。我们的分析是针对ABC分子具有足够的能量来解离A + BC而不解离A + B + C而不解离AB + C或AC + B的情况。

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