Why Does the Hydrogen-Atom Wave Function Equal R(r)cita(cita)phi(phi)?

[asdf1]

why does it equal R(r)cita(cita)phi(phi)?

 

[LeonhardEuler]

Beforehand there is nothing that tells you it does before you solve the Shrodinger equation. It is just lucky that the problem falls into the class of differential equations known as "seperable equations". You know that it does equal $R(r)\Theta (\theta) \Phi (\phi)$ because it ends up working in the equation.

 

[jtbell]

Because the Schrödinger equation for the hydrogen atom (a partial differential equation in the three variables $r, \theta, \phi$ is separable into three ordinary differential equations, one for each variable.

 

[asdf1]

thank you very much!