Journal ArticleDOI
On the Dirac Theory of Spin 1/2 Particles and Its Non-Relativistic Limit
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TLDR
In this paper, a canonical transformation on the Dirac Hamiltonian for a free particle is obtained in which positive and negative energy states are separately represented by two-component wave functions.Abstract:
By a canonical transformation on the Dirac Hamiltonian for a free particle, a representation of the Dirac theory is obtained in which positive and negative energy states are separately represented by two-component wave functions. Playing an important role in the new representation are new operators for position and spin of the particle which are physically distinct from these operators in the conventional representation. The components of the time derivative of the new position operator all commute and have for eigenvalues all values between $\ensuremath{-}c$ and $c$. The new spin operator is a constant of the motion unlike the spin operator in the conventional representation. By a comparison of the new Hamiltonian with the non-relativistic Pauli-Hamiltonian for particles of spin \textonehalf{}, one finds that it is these new operators rather than the conventional ones which pass over into the position and spin operators in the Pauli theory in the non-relativistic limit. The transformation of the new representation is also made in the case of interaction of the particle with an external electromagnetic field. In this way the proper non-relativistic Hamiltonian (essentially the Pauli-Hamiltonian) is obtained in the non-relativistic limit. The same methods may be applied to a Dirac particle interacting with any type of external field (various meson fields, for example) and this allows one to find the proper non-relativistic Hamiltonian in each such case. Some light is cast on the question of why a Dirac electron shows some properties characteristic of a particle of finite extension by an examination of the relationship between the new and the conventional position operators.read more
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Book ChapterDOI
Electron Density in Quantum Theory
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TL;DR: In this paper, the theory of the electron density in quantum chemistry and the extent to which relativistic effects are recovered by approximated many-electron Hamiltonians are discussed.
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Universal binding and recoil corrections to bound state g factors in hydrogenlike ions.
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Reference EntryDOI
Recent Advances in Relativistic Density Functional Methods
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TL;DR: Relativistic density functional theory has evolved into a powerful method for the electronic structure calculations of systems containing heavy elements as discussed by the authors, which facilitates direct and systematic comparisons between different Hamiltonians, and facilitates the construction of hybrid relativistic and non-relative methods for systems consisting of only a few heavy elements but many light ligands.
Journal ArticleDOI
Tensor operator for electron polarization
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TL;DR: In this paper, it was shown that the polarization of a free Dirac particle can be treated in a covariant way in terms of an antisymmetric second-rank tensor operator which commutes with the Hamiltonian.
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From Complex to Stochastic Potential: Heavy Quarkonia in the Quark-Gluon Plasma
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