Reduction to Two-Component Form and Picture Change Artifacts

Reduction to Two-Component Form and Picture Change Artifacts 

The unitary transformation of the Dirac Hamiltonian to two-component form is accompanied by a corresponding reduction of the wave function. As discussed in detail in chapters 11 and 12, the four-component Dirac spinor ip will 

The neglect of this mandatory transition has been referred to as the picture-change effect or picture-change error (PCE) [762,763]. It should be emphasized that this phrase can easily cause misconceptions and has been a source of confusion over the years. As a matter of fact, the PCE is not a physical effect at all but a pure artifact due to an incomplete and therefore incorrect formulation of the property expression under consideration within the two-component framework. 

In the following sections, we introduce the basic principles of the correct calculation of expectation values for a single electron moving in external fields. 

A generalization to the many-electron case and the relation to response theory is straighforward along the principles highlighted in the preceding sections. 

---