separation constant

English

Noun

separation constant (plural separation constants)

1. (calculus) 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

constant introduced after separation of variables

• German: Seperationskonstante f