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Drude formula is derived in a limited way, namely by assuming that the charge carriers form a classical ideal gas. When quantum theory is considered, the Drude model can be extended to the free electron model, where the carriers follow Fermi–Dirac distribution. The conductivity predicted is the same as in the Drude model because it does not ...
In solid-state physics, the free electron model is a quantum mechanical model for the behaviour of charge carriers in a metallic solid. It was developed in 1927, [1] principally by Arnold Sommerfeld, who combined the classical Drude model with quantum mechanical Fermi–Dirac statistics and hence it is also known as the Drude–Sommerfeld model.
Paul Drude (c. 1900) realized that the phenomenological description of conductivity can be formulated quite generally (electron-, ion-, heat- etc. conductivity). Although the phenomenological description is incorrect for conduction electrons, it can serve as a preliminary treatment.
The model is derived by modeling an electron orbiting a massive, stationary nucleus as a spring-mass-damper system. [2] [3] [4] The electron is modeled to be connected to the nucleus via a hypothetical spring and its motion is damped by via a hypothetical damper. The damping force ensures that the oscillator's response is finite at its ...
Painting of Hendrik Lorentz by Menso Kamerlingh Onnes, 1916 Portrait by Jan Veth Lorentz' theory of electrons. Formulas for the Lorentz force (I) and the Maxwell equations for the divergence of the electrical field E (II) and the magnetic field B (III), La théorie electromagnétique de Maxwell et son application aux corps mouvants, 1892, p. 451.
1902 – Max Abraham develops his classical model of the electron. It anticipated some elements of special relativity like the non-linear dependence of momentum on velocity – or, in other, more debatable terms, the relativistic mass. However, Abraham’s formula was different than in SR or in Lorentz’s theory.
While the Drude-Lorentz model of electrical conductivity makes excellent predictions about the nature of electrons conducting in metals, it can be furthered by using quantum tunnelling to explain the nature of the electron's collisions. [21] When a free electron wave packet encounters a long array of uniformly spaced barriers, the reflected ...
Valence electron, as an outer shell electron that is associated with an atom; Valence and conduction bands, as a conduction band electron relative to the electronic band structure of a solid; Fermi gas, as a particle of a non-interacting electron gas; Free electron model, as a particle in the Drude-Sommerfeld model of metals; Free-electron ...