Funções de onda radiais para  momento angular = 0 h/2π

f=DSolve[u''[r]==a u[r]/r,u,r,Assumptions->a>0]

FunctionExpand[f[[1,1]] ]

FunctionExpand[ BesselI[1,2  (Sqrt[r])]  ]

Plot[ {BesselI[1,2  (Sqrt[r])] , BesselK[1,2  (Sqrt[r])]  } ,{r,0,1},PlotStyle->{Red,Blue}]

Series[BesselI[1,2  (Sqrt[r])],{r,0,3}]

Series[BesselK[1,2  (Sqrt[r])],{r,0,3}]

Integrate[(-3Exp[-I  ϕ]+4Exp[I  ϕ])(-3Exp[I  ϕ]+4Exp[-I ϕ]),{ϕ,0,2Pi}]