Upload
zohaib-ahmed
View
399
Download
0
Embed Size (px)
Citation preview
Free electron model
In solid-state physics, the free electron model is a simple model for the behaviour of valence electrons in a crystal structure of
a metallic solid.
Drude modelThe model, which is an application of kinetic theory, assumes that the microscopic behavior of electrons in a solid may be treated classically
and looks much like a pinball machine, with a sea of constantly jittering electrons bouncing and re-bouncing off heavier, relatively
immobile positive ions.
The Drude model of electrical conduction was proposed in 1900[1][2] byPaul DrudeThe model was extended in 1905 by Hendrik Antoon Lorentz (and hence is also known
as the Drude–Lorentz model) and is a classical model.
Classical theoriesClassical theories refers to theories that predate modern, more complete, or more
widely applicable theories.
Assumptions• The Drude model considers the metal to be formed of a mass of positively-charged
ions from which a number of "free electrons" were detached.• The Drude model neglects any long-range interaction between the electron and the
ions or between the electrons.
ExplanationsDC field
simplest analysis of the Drude model assumes that• electric field E is both uniform and constant
• the thermal velocity of electrons is sufficiently high such that they accumulate only an infinitesimal amount of momentum dp between collisions, which occur on
average every τ seconds.
Time-varying analysisThe dynamics may also be described by introducing an effective drag force
Accuracy of the model• simple classical Drude model provides a very good explanation of DC
and AC conductivity in metal• it greatly overestimates the electronic heat capacities of metals
Quantum theoryquantum theory is a collection of results from the years 1900–1925 which
predate modern quantum mechanics. theory was never complete or self-consistent, but was a set
of heuristic prescriptions which are now understood to be the first quantum corrections to classical mechanics
Arnold Sommerfeld made a crucial contribution by quantizing the z-component of the angular momentum, which in the old quantum era was called space quantizationThis allowed the orbits of the electron to be ellipses instead of circles, and
introduced the concept of quantum degeneracy
Degenerate energy levelsIn quantum mechanics, an energy level is said to be degenerate if it corresponds to two or more different measurable states of a quantum system. Conversely, two or more different states of a quantum mechanical system are said to bedegenerate if
they give the same value of energy upon measurement.
The number of different states corresponding to a particular energy level is known as the degree of degeneracy of the level. It is represented mathematically by the
Hamiltonian
Bohr–Sommerfeld quantizationa procedure for selecting out certain discrete set of states of a classical integrable motion as allowed states. These are like the allowed orbits of the Bohr model of the atom; the system can only be in one of these states and not in any states in between.
Basic principleThe basic idea of the old quantum theory is that the motion in an atomic system is
quantized, or discrete.
ExamplesHarmonic oscillator