Fonones#
(418)#\[ \left(\hat{T}_n + E_i(\{\vec{R}\})\right)\Psi_n^{\gamma}\approx \sum_{\alpha} \left(\frac{\hbar^2}{2} \frac{d^2}{dQ_\alpha^2}+\frac{1}{2}K_\alpha Q_\alpha^2\right)\Psi_n^{\gamma} = E_{i,\gamma}\Psi_n^{\gamma}\]
(419)#\[\Psi_n^{\gamma}=\prod_{\alpha} \chi_\alpha (Q_\alpha)\]
(420)#\[\langle n_{a\vec{k}} \rangle = \frac{1}{e^{\frac{\hbar\omega_{a\vec{k}}}{KT}}-1}\]
Definición#
The divergence is an operator that is applied on a vector field.
(421)#\[\vec{\nabla}\cdot \vec{f}=\frac{\partial f_x}{\partial x}+\frac{\partial f_y}{\partial y}+\frac{\partial f_z}{\partial z}\]
As can be seen, the result of the applying the divergence is a scalar field.
Interpretation#
The divergence measures the difference between the number of field lines that enter and leave from/to a particular point.
Ejemplo
Fig. 210 The divergence measures the number of lines entering/exiting a point.#
A positive divergence is associated with a majority of lines coming out (leaving) from a point. This point is a source of field lines. On the other hand, a point with a negative divergence is seen to come from a majority of lines entering into a point. This point is called a sink of field line.