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Sommerfeld’s Model - Coggle Diagram

- - - - A wave function associated with a well-defined energy is an eigenfunction of the H operator with the eigenvalue being the energy.
- - - - This can be understood by dropping the free electrons of a metal one by one into the potential well.
  - - - The third electron dropped would occupy the next energy level
        
        That is, the third electron dropped would occupy the energy level E1 (> E0) and so on because of Pauli’s exclusion principle
        
        If the metal contains N (even) number of electrons, they will be distributed in the first N/2 energy levels and the higher energy levels will be completely empty.
- - - - Free & independent electrons, but no assumptions about the nature of the scattering
        
        Starting point: time-independent Schrödinger equation (TISE).
- - - - Reciprocal space is quantized in units of 2𝜋/𝐿 in all three directions kx, ky and kz, when the periodic boundary condition is employed.
        
        The Pauli exclusion principle should be applied to each electron; no two electrons can go into the same quantum state.
- - - - Arnold Sommerfeld combined the classical Drude model with quantum mechanics in the free electron model (or Drude-Sommerfeld model).
        
        Here, the electrons are modelled as a Fermi gas, a gas of particles which obey the quantum mechanical Fermi-Dirac statistics.
        
        The free electron model gave improved predictions for the heat capacity of metals, however, it was unable to explain the existence of insulators.
- - - - Without e-core and e-e interactions, the conduction electrons behave very much like independent free electrons.
        
        Each one is governed by the free electron Schrodinger equation except that the quantum level will be filled according to Pauli exclusion principle.