The FW wavefunction

The basic reason for the divergences observed at the end of the previous subsection is that there is a fundamental difference between the upper large) component g of the Dirac bispinor, and the 2-component FW spinor 

The former is only weekly, the latter strongly singular. It is an immediate consequence of the FW transformation that the FW wave function (j) is related to the Dirac function ip = (9 , x) 

We see that for small r, (f 2 differs from 2 by be. for H-like ions by —Zip jr. Similarly one finds that p4 has a r -singularity, not shared by (P4. The upper component (p of the exact Dirac eigenfunction of H-like ions behaves for small r as 

We cannot comment here on the relation of the difference between p and 

A surprisingly simple way to avoid the singularities related to the FW transformation consists in searching for a nonunitary similarity transformation of the Dirac Hamiltonian [13] 

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