27 The Fermionic Oscillator
In this chapter we’ll introduce a new quantum system by using a simple variation on techniques we used to study the harmonic oscillator, that of replacing commutators by anticommutators. This variant of the harmonic oscillator will be called a “fermionic oscillator”, with the original sometimes called a “bosonic oscillator”. The terminology of “boson” and “fermion” refers to the principle enunciated in chapter 9 that multiple identical particles are described by tensor product states that are either symmetric (bosons) or antisymmetric (fermions).
The bosonic and fermionic oscillator systems are single-particle systems, describing the energy states of a single particle, so the usage of the bosonic/fermionic terminology is not obviously relevant. In later chapters we will study quantum field theories, which can be treated as infinite dimensional oscillator systems. In that context, multiple particle states will automatically be symmetric or antisymmetric, depending on whether the field theory is treated as a bosonic or fermionic oscillator system, thus justifying the terminology.
Chapter contents
- 27.1 Canonical anticommutation relations and the fermionic oscillator
- 27.2 Multiple degrees of freedom
- 27.3 For further reading
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正文：英文 · OCR 机器稿 · 待校对
核对状态：OCR 机器稿 · 待校对
原书 PDF · 印刷页 305、306、307、308、309、310
来源版本：2025-10-20
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