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Symmetry and Asymmetry in the Mendeleïev`s Periodic Table
Symmetry and Asymmetry in the Mendeleïev`s Periodic Table

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... This is the same as a system of two equations in two unknowns with infinitely many solutions. Even though the coefficients of the unknowns are complex we solve the system of equations using the same steps as if the numbers were real. When we had reaI numbers we codd usually see right away that the t ...
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... Given the particular differential operators involved, this is a linear partial differential equation. It is also a diffusion equation, but unlike the heat equation, this one is also a wave equation given the imaginary unit present in the transient term. The time-independent Schrödinger equation is t ...
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... Few-Nucleon calculations with ∆ degrees of freedom Three- and four-nucleon systems are described allowing for the excitation of a nucleon to a Delta isobar. The excitation of the Delta isobar remains virtual; the Delta isobar is therefore considered a stable particle with zero width. It yields a two ...
Proof of the Formulae for the Molecular Orbitals and Energy Levels
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... In Frost and Musulin's mnemonie device'" for representing the RMO energy-lev el spectrum of Huckel annulenes, the regular n-gon is oriented with one vertex »down«. The phase angle of n/n by which equations (13) and (14) differ eorresponds in this eontext to a rotation of Frost and Musulin's polygon2 ...
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... To describe kinematics of some physical system or event we are free to choose units of measure of the three basic kinematical physical quantities: length (L), mass (M) and time (T). Equivalently, we may choose any three linearly independent combinations of these quantities. The choice of L, T and M ...
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Two-body Dirac equations

In quantum field theory, and in the significant subfields of quantum electrodynamics and quantum chromodynamics, the two-body Dirac equations (TBDE) of constraint dynamics provide a three-dimensional yet manifestly covariant reformulation of the Bethe–Salpeter equation for two spin-1/2 particles. Such a reformulation is necessary since without it, as shown by Nakanishi, the Bethe–Salpeter equation possesses negative-norm solutions arising from the presence of an essentially relativistic degree of freedom, the relative time. These ""ghost"" states have spoiled the naive interpretation of the Bethe–Salpeter equation as a quantum mechanical wave equation. The two-body Dirac equations of constraint dynamics rectify this flaw. The forms of these equations can not only be derived from quantum field theory they can also be derived purely in the context of Dirac's constraint dynamics and relativistic mechanics and quantum mechanics. Their structures, unlike the more familiar two-body Dirac equation of Breit, which is a single equation, are that of two simultaneous quantum relativistic wave equations. A single two-body Dirac equation similar to the Breit equation can be derived from the TBDE. Unlike the Breit equation, it is manifestly covariant and free from the types of singularities that prevent a strictly nonperturbative treatment of the Breit equation.In applications of the TBDE to QED, the two particles interact by way of four-vector potentials derived from the field theoretic electromagnetic interactions between the two particles. In applications to QCD, the two particles interact by way of four-vector potentials and Lorentz invariant scalar interactions, derived in part from the field theoretic chromomagnetic interactions between the quarks and in part by phenomenological considerations. As with the Breit equation a sixteen-component spinor Ψ is used.
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