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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.
Drude applied the kinetic theory of a dilute gas, despite the high densities, therefore ignoring electron–electron and electron–ion interactions aside from collisions. [ Ashcroft & Mermin 13 ] The Drude model considers the metal to be formed of a collection of positively charged ions from which a number of "free electrons" were detached.
The actual quantum state of the electron is entirely determined by , not k or u directly. This is important because k and u are not unique. Specifically, if ψ {\displaystyle \psi } can be written as above using k , it can also be written using ( k + K ) , where K is any reciprocal lattice vector (see figure at right).
The nearly-free electron debacle compelled researchers to modify the assumpition that ions flowed in a sea of free electrons. A number of quantum mechanical models were developed, such as band structure calculations based on molecular orbitals, and the density functional theory. These models either depart from the atomic orbitals of neutral ...
Dispersion relation for the 2D nearly free electron model as a function of the underlying crystalline structure. The nearly free electron model is a modification of the free-electron gas model which includes a weak periodic perturbation meant to model the interaction between the conduction electrons and the ions in a crystalline solid.
A 1906 proposal to change to electrion failed because Hendrik Lorentz preferred to keep electron. [25] [26] The word electron is a combination of the words electric and ion. [27] The suffix -on which is now used to designate other subatomic particles, such as a proton or neutron, is in turn derived from electron. [28] [29]
Note that the "perturbation" term ′ gets progressively smaller as k approaches zero. Therefore, k·p perturbation theory is most accurate for small values of k . However, if enough terms are included in the perturbative expansion , then the theory can in fact be reasonably accurate for any value of k in the entire Brillouin zone .
Free electron in physics may refer to: Electron, as a free particle; Solvated electron; Charge carrier, as carriers of electric charge; 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