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 schrodinger 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 schrodinger 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.