Question

What are radial and angular wave function in schrodinger wave equation?

Answer 1

Explanation:

Schrodinger wave equation for h atom& hydrogen like atom is

(d^2/dx^2+d^2/dy^2+d^2/dz^2)psi+8π^2m/h^2(E+e^2/r)psi=0 ------(1)

Take a point a coordinate x,y,z in space.

Let OA=r that is distance from the nucleus & theta &phai be the angle.

z=ON=rcos theta

y=OM=LK=OLsin phai

x=OK=OLcosphai

thus equation (1)can be written in terms of polar coordinate as follows.

1/r^2d/dr{r^2d psi(r,theta,phai)/dr}+1/r^2sintheta d/dtheta{sin theta d psi(r,theta,phai)/d theta}+1/r^2sin^2phai.d^2psi(r,theta,phai)/d (psi)^2+8π^2mu/h^2(E+e^2/r)psi(r,theta,phai)=0