从Fock空间到Hilbert空间的往返：通勤者指南
Back and forth from Fock space to Hilbert space: a guide for commuters
摘要：
由许多相同粒子组成的系统的量子态，例如费米-哈伯德模型和玻色-哈伯德模型所描述的那些，可以方便地在Fock空间中描述。然而，为了评估某些特定的可观测量或研究系统动力学，它往往是更有效地采用希尔伯特空间描述。因此，有效地从一种描述转移到另一种描述是一个理想的特征，特别是当需要数值方法时。在这里，我们回顾了Fock空间的结构不可区分的粒子系统，然后提出了一套食谱和建议，为那些学生和研究人员在需要往返于一个描述到另一个。两个粒子的情况下，讨论了一些细节，并给出了一些数值实现的指导方针。
英文摘要：
Quantum states of systems made of many identical particles, e.g. those described by Fermi-Hubbard and Bose-Hubbard models, are conveniently depicted in the Fock space. However, in order to evaluate some specific observables or to study the system dynamics, it is often more effective to employ the Hilbert space description. Moving effectively from one description to the other is thus a desirable feature, especially when a numerical approach is needed. Here we recall the construction of the Fock space for systems of indistinguishable particles, and then present a set of recipes and advices for those students and researchers in the need to commute back and forth from one description to the other. The two-particle case is discussed in some details and few guidelines for numerical implementations are given.
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