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The s electrons are again assumed to occupy the axial positions while the f electrons occupy the positions at the vertices of two heptagonal bases of the two constituent pyramids. While these results are interesting, they have been contested in the scientific literature due to Luder's abandonment of the octet rule and the author's controversial ...
The Lindblad master equation describes the evolution of various types of open quantum systems, e.g. a system weakly coupled to a Markovian reservoir. [1] Note that the H appearing in the equation is not necessarily equal to the bare system Hamiltonian, but may also incorporate effective unitary dynamics arising from the system-environment ...
The equations for relativistic quantum fields, of which the Klein–Gordon and Dirac equations are two examples, can be obtained in other ways, such as starting from a Lagrangian density and using the Euler–Lagrange equations for fields, or using the representation theory of the Lorentz group in which certain representations can be used to ...
In this way, the electrons of an atom or ion form the most stable electron configuration possible. An example is the configuration 1s 2 2s 2 2p 6 3s 2 3p 3 for the phosphorus atom, meaning that the 1s subshell has 2 electrons, the 2s subshell has 2 electrons, the 2p subshell has 6 electrons, and so on.
The equations themselves are called "wave equations" or "field equations", because they have the mathematical form of a wave equation or are generated from a Lagrangian density and the field-theoretic Euler–Lagrange equations (see classical field theory for background).
This approach is called "post-Newtonian" because the Newtonian solution for the particle orbits is often used as the initial solution. The theory can be divided into two parts: first one finds the two-body effective potential that captures the GR corrections to the Newtonian potential. Secondly, one should solve the resulting equations of motion.
The Bethe formula is only valid for energies high enough so that the charged atomic particle (the ion) does not carry any atomic electrons with it. At smaller energies, when the ion carries electrons, this reduces its charge effectively, and the stopping power is thus reduced. But even if the atom is fully ionized, corrections are necessary.
For example, in a collision between electrons and molecules, there may be tens or hundreds of particles involved. But the phenomenon may be reduced to a two-body problem by describing all the molecule constituent particle potentials together with a pseudopotential. [5] In these cases, the Lippmann–Schwinger equations may be used.