Rotación molecular#
(319)#\[T_\text{rot}=\frac{1}{2}\sum_{xy}\frac{1}{I_{xy}}\hat{J}_x \hat{J}_y ~~~~\text{donde} ~~~~~ I_{xy}=\sum_\alpha M_\alpha R_{\alpha,x} R_{\alpha,y} ~~\text{tensor inercia}\]
(320)#\[T_\text{rot}=\frac{1}{2}\sum_{q}\frac{1}{I_{q}}\hat{J}_q^2\]
(321)#\[\hat{J}^2 \rightarrow \hbar^2 J(J+1)\]
(322)#\[\hat{H}=\frac{\hat{\vec{J}}^2}{2I} \rightarrow E_J=\frac{\hbar^2}{2I}J(J+1) = B J(J+1),~ J=0,1,2...\]
(323)#\[E_{J+1}-E_{J}=2B(J+1), J=0,1,2,\cdots\]
(324)#\[\hat{H}=\frac{\hat{J}_x^2+\hat{J}_y^2}{2I_\perp}+\frac{\hat{J}_z^2}{2I_\parallel}=\frac{\hat{J}^2}{2I_\perp}+\hat{J}_z^2\left(\frac{1}{2I_\parallel}-\frac{1}{2I_\perp}\right)\]
(325)#\[E(J,K)=J(J+1) \frac{\hbar^2}{2I_\perp}+K^2 \hbar^2 \left(\frac{1}{2I_\parallel}-\frac{1}{2I_\perp}\right)=B^\prime J(J+1)+(A^\prime-B^\prime)K^2\]
Definición#
The divergence is an operator that is applied on a vector field.
(326)#\[\vec{\nabla}\cdot \vec{f}=\frac{\partial f_x}{\partial x}+\frac{\partial f_y}{\partial y}+\frac{\partial f_z}{\partial z}\]
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. 203 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.