For the hydrogen atom the $($not normalised$)$ radial wave function Rn$,$l$($r$)$ is

given by the expression

Rn$,$l$($r$)=$ e

$$r$/($na$0)$

s

X$=$n$1$

s$=$l

csr

s

$,$

where cl $=1$ without loss of generality. Using the recurrence relation

cs$[$s$($s $+1)$ l$($l $+1)]=2$

s

a

$$

$1$

a$0$

cs$1$

with a $=$ na$0,$ show that the radial wave functions R$1,0($r$)$ and R$2,0($r$)$ are as

follows:

R$1,0($r$)=$ e

$($r$/$a$0)$

and R$2,0($r$)=(1$ r$/[2$a$0])$ e

$($r$/[2$a$0])$