⎧ 0   r<a
V = ⎨
    ⎩ ∞   r>a

    for r<a
    ───────
    
    ∂͟²͟ R + 2͟ ∂͟ R -  1͟  l(l+1) K²R = 0
    ∂ρ²    r ∂r     2r²       
    
    K ≡ √⎛2͟m͟E͟⎞  ρ ≡ Kr
         ⎝ ħ²⎠

    ⇒ ∂͟²͟ R + 2͟ ∂͟ R - ⎛ 1͟ l(l+1) - 1 ⎞ R = 0
      ∂ρ²    ρ ∂r    ⎝ ρ²           ⎠

    The solutions are Bessel functions


       ⎧ jₗ(ρ) = (-ρ)ˡ ⎛1͟ d͟ ⎞ˡ⎛s͟i͟n͟ρ͟⎞
       ⎪               ⎝ρ dρ⎠ ⎝  ρ ⎠    (regular)
R(ρ) = ⎨
       ⎪ nₗ(ρ) = -(-ρ)ˡ ⎛1͟ d͟ ⎞ˡ⎛c͟o͟s͟ρ͟⎞   ⎛ irregular or      ⎞
       ⎩                ⎝ρ dρ⎠ ⎝  ρ ⎠   ⎝ "Neuman function" ⎠

For continuity

   
⎧
⎪ A sin(K₀ a) = C e⁻ᵃ  
⎨
⎪ K₀Acos(K₀ a) = -ᵩ 
⎩