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Algebra II: Quadratic equations
Algebra II: Quadratic equations

... Step 4. Find the point(s) where the function intersects the x-axis. Step 5. Press 2nd and then GRAPH to get the table. Step 6. Find the zero value(s) of the y-variable. Step 7. Record the corresponding x-value(s) as your root(s). ( If the entire curve cannot be seen, it may be necessary to expand yo ...
Systems of equations and the elimination method
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Limits of fractality: Zeno boxes and relativistic particles
Limits of fractality: Zeno boxes and relativistic particles

... process, this would seem a limiting time interval, which in turn implies that the particle does not have fractal structure below the scale of its Compton wavelength. It would thus appear that the QZE plus a causality-like condition are enough to fix λC as a lower level of fractality. As we will see, ...
Energy absorption by “sparse” systems: beyond linear response theory Doron Cohen
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On the Extra Anomalous Gyromagnetic Ratio of the Electron and
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... the Electron, that is g = 2, which can not be accounted for using non-relativistic QM. For several years after it’s discovery, most physicists believed that it described the Proton and the Neutron as-well, which are both spin-1/2 particles. In simple terms, it was thought or presumed that the Dirac ...
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Spin Angular Momentum and the Dirac Equation

... backward and forward directions, respectively. The two directions of wave propagation are clearly independent states, and they are separated in space by a 180◦ rotation. This property is the fundamental characteristic of spin one-half functions. Generalization to three dimensional space should there ...
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... Define a variable. Then translate each sentence into an equation. Then find each number. 1. Five more than twice a number is 7. 2. Fourteen more than three times a number is 2. 3. Seven less than twice a number is 5. 4. Two more than four times a number is –10. 5. Eight less than three times a numbe ...
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Solving Linear Equations - A Mathematical Mischief Tutorial

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Exact Solutions for Non-Hermitian Dirac

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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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