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Mind Map 6 - Coggle Diagram
Mind Map 6
Sommerfeld's Model
Electronic properties
- model of electrical conduction was the Drude model, which applied kinetic theory to the electrons in a solid
- assuming that the material contains immobile positive ions and an "electron gas" of classical, non-interacting electrons, the Drude model
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The Schrödinger equation
- Classical mechanics fails in describing motion at the atomic and molecular scales and is simply incorrect
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- Schrödinger used the Hamilton’s equation as the basis of quantum mechanics
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Free electron in box
- the wave function 𝜓(x, y, z) must be zero
- An application of the boundary condition 𝜓(0) = 0 and 𝜓(L) = 0 to Schrodinger’s equation for a single free electron
- Each one is governed by the free electron Schrodinger equation except that the quantum level
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Fermi sphere
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- The k-space sphere with radius kF is called the Fermi sphere
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Band theory
Bloch's Waves
- According to Bloch's theorem, the wavefunction solution of the Schrödinger equation when the potential is periodic, can be written as Ψ(𝑥) = 𝑒𝑖𝑘𝑥𝑢(𝑥) where 𝑢(𝑥) is a periodic function which satisfies 𝑢(𝑎 + b) = 𝑢(𝑥).
- to find a solution for a single period, make sure it is continuous and smooth, and to make sure the function 𝑢(𝑥) is also continuous and smooth
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Effective Mass
- same magnitude of electric field is applied to both electrons in vacuum and inside the crystal
- electron inside the crystal has to try to make its own way
- the electrons inside the crystal will have a different mass than that of the electron in vacuum
- altered mass is called as an effective-mass
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