Seperation of variables in the Schrodinger equation

[Sonko]

hey guys first post so sorry if this has already been asked :S

what exactly is meant by the separation of variables in the Schrödinger equation? also what co-ordinate system would i use to solve for an electron in a hydrogen-like ion?

thanks

 

[Hootenanny]

hey guys first post so sorry if this has already been asked :S

what exactly is meant by the separation of variables in the Schrödinger equation? also what co-ordinate system would i use to solve for an electron in a hydrogen-like ion?

thanks

Welcome to Physics Forums, Sonko.

Separation of variable is a technique used to solve differential equations. In terms of partial differential equations one would assume that a function of two variables, say $\Psi\left(x,t\right)$ can be written as a product of two functions of single variables, say $\psi\left(x\right)$ and $\phi\left(t\right)$. If this assumption is applicable, i.e. if the equation is separable, you can reduce the partial differential equation for two variables into two ordinary differential equations for one variable - one equation for each function and associated variable. Try search for "separation of variables" for more information.

In terms of solving the Schrödinger equation for hydrogen-like ions, you will have a spherically symmetric potential. Therefore, it will be best to solve Schrödinger's equation in spherical coordinates.