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MIND MAP 3, image, ADIBAH HANISAH BINTI SAMSUDIN A19SC0002 991022-04…

- - - - determine the maximum vibration frequency
        
        at low T
        
        this model is exact at low and high T and an interpolation formula in between
    - - periodic boundary conditions that require a wave function on certain bravais lattice to be periodic
    - - the average thermal energy of an oscillator of frequency
      - high T behavior is good
        
        the behavior at T=0
        
        at low T
- - - - wave eqn solution still satisfies
        
        the details form of the dispersion relation is changed but ω is still periodic function of k with period 2π/a
        
        group velocity vanishes at k=(±)π/a