Normal coordinates diatomic chain

This text of the two-volume treatment contains most of the theoretical background necessary to understand experiments in the field of phonons. This background is presented in four basic chapters. Chapter 2 starts with the diatomic linear chain. In the classical theory we discuss the periodic boundary conditions, equation of motion, dynamical matrix, eigenvalues and eigenvectors, acoustic and optic branches and normal coordinates. The transition to quantum mechanics is achieved by introducing the Sohpddingev equation of the vibrating chain. This is followed by the occupation number representation and a detailed discussion of the concept of phonons. The chapter ends with a discussion of the specific heat and the density of states. 

From (2.62) it immediately follows that ,(" ) = ai( ) and ao( ) = - < p( )> SO that only half of the real normal coordinates a (p are independent and we have as many independent normal coordinates as there are degrees of freedom (2N for the longitudinal modes of the diatomic chain with N unit cells). The independent normal coordinates thus obtained by restricting... 

As in the case of the diatomic chain, it is possible to introduce real normal coordinates a (j) (standing waves) or n(j) (running waves). They are defined by expressions analogous to (2.62,67), respectively. 

C) Hamiltonian for the Diatomic Chain in Terms of Normal Coordinates... 

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