Asymptotic Behavior

As ρ→∞, the second and third terms in the bracket reduce to zero, and the equation reduces to following form:

The general solution is:

since eρ→∞ as ρ→∞, thus B = 0, and

.......(i)

However, in Equation (i), for ρ→0, the angular momentum term dominates, and approximately the equation reduces to the following form:

The general solution is:

Since ρ−l→∞ as ρ→0, thus D = 0, and the solution reduces to: