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The definitions for monopoles are of theoretical interest, although real magnetic dipoles can be described using pole strengths. There are two possible units for monopole strength, Wb (Weber) and A m (Ampere metre). Dimensional analysis shows that magnetic charges relate by q m (Wb) = μ 0 q m (Am).
In electromagnetism, and because of relativistic invariance, it is useful to have the electric field E and the magnetic field B in the same unit , using the cgs (Gaussian) system of units, where energy is given in units of erg, mass in grams (g), and momentum in g·cm·s −1.
The first two-dimensional spin matrices (better known as the Pauli matrices) were introduced by Pauli in the Pauli equation; the Schrödinger equation with a non-relativistic Hamiltonian including an extra term for particles in magnetic fields, but this was phenomenological.
The potential energy of the interaction between the two electrons in orthogonal orbitals can be represented by a matrix, say . From Eq. (3), the characteristic values of this matrix are . The characteristic values of a matrix are its diagonal elements after it is converted to a diagonal matrix (that is, eigenvalues).
The two-body problem in general relativity (or relativistic two-body problem) is the determination of the motion and gravitational field of two bodies as described by the field equations of general relativity. Solving the Kepler problem is essential to calculate the bending of light by gravity and the motion of a planet orbiting its sun.
Electron energy loss spectroscopy (EELS) is a form of electron microscopy in which a material is exposed to a beam of electrons with a known, narrow range of kinetic energies. Some of the electrons will undergo inelastic scattering , which means that they lose energy and have their paths slightly and randomly deflected.
At low energy, the energy loss according to the Bethe formula therefore decreases approximately as v −2 with increasing energy. It reaches a minimum for approximately E = 3 Mc 2 , where M is the mass of the particle (for protons, this would be about at 3000 MeV).
In this case net energy may be transferred from the electron to the photon. The inverse Compton effect is seen in astrophysics when a low energy photon (e.g. of the cosmic microwave background) bounces off a high energy (relativistic) electron. Such electrons are produced in supernovae and active galactic nuclei. [26]