Separation constant

English

Noun

1. Template:Lb a constant that may be introduced upon separation of variables

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

Translations

• German: Template:T