Main Question or Discussion Point
The Schrodinger wavefunction for the hydrogen atom scales as r^l for small r, where l is the orbital angular momentum. Is this changed in any dramatic way for the Dirac equation wavefuction? Does the small component of the Dirac spinor have the same small-r asymptotic behaviour as the large component? Can someone tell me the small r behaviour for the 1S j=1/2 state and 2P j=1/2,3/2 states? Thanks in advance.