Item
Karwowski, Jacek  
2010 July 8  
Several unexpected properties of the Dirac equation, related to its multicomponent structure and unboundedness from below of the Dirac Hamiltonian are discussed. In particular, a pathological behaviour of an exact density functional derived from either Dirac or LevyLeblond equation is presented. For a oneelectron atom, as one should expect, the variational minimum of this functional gives the exact ground state energy and corresponds to the correct density. However, the same minimum is also reached by an infinite set of densities which do not correspond to the exact wavefunction. Some of the wavefunctions corresponding to the correct minimum are orthogonal to the exact one. It also appears that imposing the correct boundary conditions does not remove the fake solutions. As it is known, the twoelectron DiracCoulomb equation does not have squareintegrable solutions if the interaction term is present in the Hamiltonian. As a result, all the states of twoelectron atoms, including the ground states are, from the formal point of view, autoionizing and should be treated using theoretical methods appropriate for the description of resonances. Some consequences of this facts are discussed. Transformations of the Dirac equation in the spinor space supply another degree of freedom in structuring methods of solving this equation. It appears that some nonstandard representations of the Dirac equation may be more convenient in numerical applications and result in more stable variational procedures. Several examples are discussed  
audio/mpeg video/H263 

Karwowski, J. (2010). Unexpected features of relativistic models. A â€™IX Girona Seminarâ€™. Girona: Universitat. [Consulta 7 setembre 2010]. Disponible a: http://hdl.handle.net/10256.1/1733  
http://hdl.handle.net/10256.1/1733  
eng  
Universitat de Girona. Departament de QuÃmica Universitat de Girona. Institut de QuÃmica Computacional 

IX Girona Seminar  
Aquest document estÃ subjecte a una llicÃ¨ncia Creative Commons: Reconeixement  No comercial  Compartir igual (byncsa)  
http://creativecommons.org/licenses/byncsa/3.0/es/deed.ca  
QuÃmica quÃ ntica  Congressos
Quantum chemistry  Congresses 

Unexpected features of relativistic models  
info:eurepo/semantics/lecture  
DUGiMedia 