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The tree model requires languages to evolve exclusively through social splitting and linguistic divergence. In the “tree” scenario, the adoption of certain innovations by a group of dialects should result immediately in their loss of contact with other related dialects: this is the only way to explain the nested organisation of subgroups imposed by the tree structure.
Louis de Broglie's early results on the pilot wave theory were presented in his thesis (1924) in the context of atomic orbitals where the waves are stationary.Early attempts to develop a general formulation for the dynamics of these guiding waves in terms of a relativistic wave equation were unsuccessful until in 1926 Schrödinger developed his non-relativistic wave equation.
Atomic orbitals are basic building blocks of the atomic orbital model (or electron cloud or wave mechanics model), a modern framework for visualizing submicroscopic behavior of electrons in matter. In this model, the electron cloud of an atom may be seen as being built up (in approximation) in an electron configuration that is a product of ...
Thomas–Fermi model Orbital-free density functional theory Linearized augmented-plane-wave method Projector augmented wave method: Electronic band structure; Nearly free electron model Tight binding Muffin-tin approximation k·p perturbation theory Empty lattice approximation GW approximation Korringa–Kohn–Rostoker method
De Broglie, in his 1924 PhD thesis, [8] proposed that just as light has both wave-like and particle-like properties, electrons also have wave-like properties. His thesis started from the hypothesis, "that to each portion of energy with a proper mass m 0 one may associate a periodic phenomenon of the frequency ν 0 , such that one finds: hν 0 ...
A similar atom interferometer forms the heart of the Compton clock. However, this claimed interpretation of the interferometry function has been criticised. One criticism is that a real Compton oscillator or matter wave does not appear in the design of any actual experiment. [6] The matter wave interpretation is also said to be flawed. [4] [5]
The Schrödinger equation for the electron in a hydrogen atom (or a hydrogen-like atom) is = where is the electron charge, is the position of the electron relative to the nucleus, = | | is the magnitude of the relative position, the potential term is due to the Coulomb interaction, wherein is the permittivity of free space and = + is the 2-body ...
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