Thekey difference between free electron model and nearly free electron model是自由电子模型不考虑account the electron interactions and the potential, whereas the nearly free electron model takes into account the potential.
Free electron model is a量子机械模型that is useful in describing the behaviour of the charge carriers in a金属固体. Nearly free electron model is a quantum mechanical model that describes the physical properties of electrons that are moving nearly freely through a水晶格子of a solid.
内容
1.Overview and Key Difference
2.What is Free Electron Model
3.什么是几乎免费的电子模型
4.Similarities – Free Electron Model and Nearly Free Electron Model
5.自由电子模型与表格形式的几乎免费电子模型
6。摘要 - 免费电子模型与几乎免费电子模型
什么是免费电子模型？
Free electron model is a quantum mechanical model that is useful in describing the behaviour of the charge carriers in a metallic solid. This model was developed in 1927 by Arnold Sommerfeld. He combined the classical Drude model with quantum mechanical Fermi-Dirac statistics; therefore, it was named as Drude-Sommerfeld model as well.
It is a very simple model, but it is useful in explaining many experimental findings, including the Wiedemann-Franz law, which relates the electrical conductivity and thermal conductivity, the temperature dependence of electron heat capacity, the shape of the electronic density of states, electrical conductivities, the range of binding energy values, etc. Moreover, this model solves the inconsistencies related to the Drude model, giving an insight into several properties of metals. In addition, this model is predictive when applying it for alkali and noble metals.
在考虑自由电子模型的想法和假设时，有四个主要假设。（1）自由电子近似，它描述了除边界条件以外的离子和价电子之间相互作用的否认，（2）独立电子近似，该近似描述了电子之间的相互作用，（3）近似，它描述了某些未知的散射机制，即碰撞的电子概率与松弛时间成反比，并且（4）保利排除原则，描述系统的每个状态只能占据单个电子。
The name “free electron model” originates from the first two assumptions given above, which describe that electrons act as free particles with a respective quadratic relation between the energy and the momentum.
什么是几乎免费的电子模型？
Nearly free electron model is a quantum mechanical model that describes the physical properties of electrons that are moving nearly freely through a crystal lattice of a solid. This model is very related to the empty lattice approximation. We can name this model as NFE model or quasi-free electron model. It enables the understanding and calculating of the electronic band structure of metals. Moreover, we can identify this model as an improvement of the free electron model.
我们可以将几乎免费的电子模型识别为自由电子模型的修改。与自由电子模型相似，该模型也没有考虑到电子电子相互作用（独立电子近似）。
What are the Similarities Between Free Electron Model and Nearly Free Electron Model?
- Both models are important in quantum mechanics.
- These models describe the behaviour of electrons in systems.
- They use the independent electron approximation.
游离电子模型和几乎免费电子模型有什么区别？
The free electron model is a quantum mechanical model that is useful in describing the behavior of the charge carriers in a metallic solid. Meanwhile, the nearly free electron model is a quantum mechanical model that describes the physical properties of electrons that are moving nearly freely through a crystal lattice of a solid. The key difference between free electron model and nearly free electron model is that the free electron model does not take into account the electron interactions and the potential, whereas the nearly free electron model takes into account the potential.
The following table summarizes the difference between free electron model and nearly free electron model.
摘要 - 免费电子模型与几乎免费电子模型
Free electron model is a quantum mechanical model that is useful in describing the behavior of the charge carriers in a metallic solid. The nearly free electron model is a quantum mechanical model which describes the physical properties of electrons that are moving nearly freely through a crystal lattice of a solid. The key difference between free electron model and nearly free electron model is that free electron model does not take into account the electron interactions and the potential, whereas the nearly free electron model takes into account the potential.
Reference:
1.“”Tight Binding and Nearly Free Electrons。”打开固态笔记.
Image Courtesy:
1.“”Free-electron DOS”Pieter Kuiper - 通过Commons Wikimedia自己的作品（公共领域）
2. “空晶格 - approximation-fcc波段” By Eg-T2g – Own work(CC BY-SA 3.0)通过Commons Wikimedia
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