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Dirac theory

Similarides Between Potential Ruid Dynamics and Quantum Mechanics Electrons in the Dirac Theory The Nearly Nonrelativistic Limit The Lagrangean-Density Correction Term Topological Phase for Dirac Electrons What Have We Learned About Spinor Phases ... [Pg.94]

Section VI shows the power of the modulus-phase formalism and is included in this chapter partly for methodological purposes. In this formalism, the equations of continuity and the Hamilton-Jacobi equations can be naturally derived in both the nonrelativistic and the relativistic (Dirac) theories of the electron. It is shown that in the four-component (spinor) theory of electrons, the two exha components in the spinor wave function will have only a minor effect on the topological phase, provided certain conditions are met (nearly nonrelativistic velocities and external fields that are not excessively large). [Pg.101]

The earliest appearance of the nonrelativistic continuity equation is due to Schrodinger himself [2,319], obtained from his time-dependent wave equation. A relativistic continuity equation (appropriate to a scalar field and formulated in terms of the field amplitudes) was found by Gordon [320]. The continuity equation for an electron in the relativistic Dirac theory [134,321] has the well-known form [322] ... [Pg.159]

In concluding this section we briefly establish the connection between the Dirac theory for a single isolated free particle described in the previous section and the present formalism. If T> is the state vector describing a one-particle state, iV T> = 1 T> consider the amplitude... [Pg.546]

For liquid metals, one has to set up density functionals for the electrons and for the particles making up the positive background (ion cores). Since the electrons are to be treated quantum mechanically, their density functional will not be the same as that used for the ions. The simplest quantum statistical theories of electrons, such as the Thomas-Fermi and Thomas-Fermi-Dirac theories, write the electronic energy as the integral of an energy density e(n), a function of the local density n. Then, the actual density is found by minimizing e(n) + vn, where v is the potential energy. Such... [Pg.39]

Covariant elements, molecular systems modulus-phase formalism, Dirac theory electrons, 267-268... [Pg.73]

Dirac theory, molecular systems, modulus-phase formalism ... [Pg.74]

Dirac theory, 266—268 nonrelativistic states, 263- 265 Electron spin, permutational symmetry, 711-712 Electron transfer ... [Pg.76]

The appearance of negative energy states was initially considered to be a fatal flaw in the Dirac theory, because it renders all positive energy states... [Pg.227]

Awkward questions about the electromagnetic and gravitational fields of infinitely many particles in the vacuum remain unanswered. Also, the Dirac theory, amended by the hole proposition is certainly not a one-particle theory, and hence not a relativistic generalization of Schrodinger s equation. [Pg.228]

Nonrelativistic quantum chemistry has been discussed so far. But transition metal (starting already from the first row) and actinide compounds cannot be studied theoretically without a detailed account of relativity. Thus, the multiconfigurational method needs to be extended to the relativistic regime. Can this be done with enough accuracy for chemical applications without using the four-component Dirac theory Much work has also been done in recent years to develop a reliable and computationally efficient four-component quantum chemistry.25,26 Nowadays it can be combined, for example, with the CC approach for electron correlation. The problem is that an extension to multiconfigurational... [Pg.257]

The theory of including magnetic perturbations has been discussed earlier.(11,14-16) In Dirac theory, external fields appear through the operator... [Pg.63]

Variational Principle in the Dirac Theory Theorems, Examples and Counterexamples... [Pg.177]

Variational principle in the Dirac theory theorems, examples and counter- 177 examples... [Pg.431]

The Dirac-Pauli representation is most commonly used in all applications of the Dirac theory to studies on electronic structure of atoms and molecules. Apart of historical reasons, there are several features of this representation which make its choice quite natural. Probably the most important is a well defined symmetry of and in the case of spherically-symmetric potentials V. The Dirac Hamiltonian... [Pg.219]


See other pages where Dirac theory is mentioned: [Pg.162]    [Pg.305]    [Pg.307]    [Pg.239]    [Pg.226]    [Pg.98]    [Pg.198]    [Pg.266]    [Pg.253]    [Pg.370]    [Pg.372]    [Pg.395]    [Pg.398]    [Pg.179]    [Pg.181]    [Pg.183]    [Pg.185]    [Pg.189]    [Pg.193]    [Pg.179]    [Pg.181]    [Pg.183]    [Pg.185]    [Pg.189]    [Pg.193]    [Pg.30]    [Pg.126]   
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Density Functional Theory and the Dirac-Coulomb Hamiltonian

Dirac equation electromagnetic theory

Dirac equation quantum light theory

Dirac equation relativistic theory

Dirac equation theory

Dirac hole theory

Dirac many-particle theory

Dirac theory energy surfaces

Dirac theory representation

Dirac theory structure

Dirac theory, molecular systems, modulus-phase

Dirac theory, molecular systems, modulus-phase formalism

Dirac-Breit theory

Dirac-Coulomb theory

Dirac-Gaunt theory

Dirac-Hartree-Fock theory

Diracs Theory of the Electron

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First-Quantized Dirac-Based Many-Electron Theory

Hydrogens Challenge to Dirac Theory Quantum

Interpretation of Negative-Energy States Diracs Hole Theory

Kramers-Heisenberg-Dirac theory

Modulus-phase formalism, Dirac theory

Modulus-phase formalism, Dirac theory electrons

Raman scattering Kramers-Heisenberg-Dirac theory

The Kramers-Heisenberg-Dirac Theory

The hydrogen-like atom in Dirac theory

Thomas-Fermi-Dirac theory

Variation principle in the Dirac theory

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