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Fine and hyperfine structure in hydrogen (not to scale). This section presents a relatively simple and quantitative description of the spin–orbit interaction for an electron bound to a hydrogen-like atom, up to first order in perturbation theory, using some semiclassical electrodynamics and non-relativistic quantum mechanics.
The Kohn-Sham equations are a set of mathematical equations used in quantum mechanics to simplify the complex problem of understanding how electrons behave in atoms and molecules. They introduce fictitious non-interacting electrons and use them to find the most stable arrangement of electrons, which helps scientists understand and predict the ...
Top: The charge is at rest in frame F, so this observer sees a static electric field.An observer in another frame F ′ moves with velocity v relative to F, and sees the charge move with velocity −v with an altered electric field E due to length contraction and a magnetic field B due to the motion of the charge.
For example, the nitrogen atom ground state has three unpaired electrons of parallel spin, so that the total spin is 3/2 and the multiplicity is 4. The lower energy and increased stability of the atom arise because the high-spin state has unpaired electrons of parallel spin, which must reside in different spatial orbitals according to the Pauli ...
The Klein–Gordon equation, + =, was the first such equation to be obtained, even before the nonrelativistic one-particle Schrödinger equation, and applies to massive spinless particles. Historically, Dirac obtained the Dirac equation by seeking a differential equation that would be first-order in both time and space, a desirable property for ...
By introducing the coordinate vector X of the center of mass as three of the degrees of freedom of the system and eliminating the coordinate vector of one (arbitrary) particle, so that the number of degrees of freedom stays the same, one obtains by a linear transformation a new set of coordinates t i.
At relativistic electron velocity the geometrical electron optical equations rely on an index of refraction that includes both the ratio of electron velocity to light / = and , the component of the magnetic vector potential along the electron direction: [1]: 754 = + where , , and are the electron mass, electron charge, and the speed of light ...
A birefringent crystal is a material that has an optic axis with the property that the light has a different index of refraction for light polarized parallel to the axis than it has for light polarized perpendicular to the axis. Light polarized parallel to the axis are called "extraordinary rays" or "extraordinary photons", while light ...