separation constant

Noun

 * 1)  a constant that may be introduced upon separation of variables
 * The partial differential equation $$a \sin^2 (\theta) \Phi(\phi)+\Phi(\phi)\cos (\theta) \frac{\partial \Theta(\theta)}{\partial \theta}+\frac{\partial^2 \Phi}{\partial \phi^2}=0$$ can be rewritten $$ a \sin^2 (\theta)+\cos (\theta) \frac{\partial \Theta(\theta)}{\partial \theta}=-\frac{1}{\Phi(\phi)}\frac{\partial^2 \Phi}{\partial \phi^2}\equiv K$$, where $$K$$ is a separation constant that depends on neither $$\theta$$ nor $$\phi$$. This then yields two ordinary differential equations.

Translations

 * German: Seperationskonstante