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
Citations
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Time in quantum mechanics: a story of confusion
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Gravitational geometric phase in the presence of torsion
TL;DR: In this paper, the relativistic and non-relativistic quantum dynamics of a neutral spin-1/2 particle subject to an external electromagnetic field in the presence of a cosmic dislocation are investigated.
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Dirac-exact relativistic methods: the normalized elimination of the small component method
TL;DR: In this article, a general 1-component normalized elimination of the small component (NESC) algorithm is presented for the calculation of reliable energies, geometries, electron density distributions, electric moments, electric field gradients, hyperfine structure constants, contact densities and Mossbauer isomer shifts.
Journal ArticleDOI
What is the relativistic spin operator
TL;DR: In this article, the authors investigated the properties of different spin operators and showed that most candidates are lacking essential features of proper angular momentum operators, leading to spurious zitterbewegung (quivering motion) or violation of the angular momentum algebra.
Journal ArticleDOI
Predicting Near Edge X-ray Absorption Spectra with the Spin-Free Exact-Two-Component Hamiltonian and Orthogonality Constrained Density Functional Theory.
TL;DR: A novel implementation of the spin-free exact-two-component (X2C) one-electron treatment of scalar relativistic effects and its combination with a recently developed OCDFT approach to compute a manifold of core-valence excited states is reported.
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