Finite Spherical Well and Deuterium Nucleus

    Attractive potential exists between proton and neutron

    (pic) step function potential

    Assume l=0 then S.E. for radial function is

        −͟ħ͟²͟ ⎛∂͟²͟ R + 2͟ ∂͟ R⎞V R = E R
         2m ⎝∂r²    r ∂r ⎠

    K² ≡ (E͟_͟−͟_͟V͟)2m  ⇒  ∂͟²͟ R + 2͟ ∂͟ R + K² R = E R 
            ħ²         ∂r²    r ∂r  

    R(r) = U(r)/r  ⇒  ∂͟²͟ U = - K² R
                      ∂r²  

For r<a

K₀ = 2͟m͟(E+V₀) ⇒ 
     ħ²