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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 ...
In the early 19th century, Thomas Young and August Fresnel clearly demonstrated the interference and diffraction of light, and by 1850 wave models were generally accepted. [45] James Clerk Maxwell 's 1865 prediction [ 46 ] that light was an electromagnetic wave – which was confirmed experimentally in 1888 by Heinrich Hertz 's detection 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 ...
This experiment was noted for extending the applicability of wave–particle duality by about one order of magnitude in the macroscopic direction. [25] In 2009, researchers from IBM managed to take the first picture of a real molecule. [26] Using an atomic force microscope every single atom and bond of a pentacene molecule could be imaged.
An atom interferometer uses a small difference in waves associated with two atoms to create an observable interference pattern. Conventionally these waves are associated with the electrons orbiting the atom, but the matter wave theory suggests that the wave associated with the wave–particle duality of the atom itself may alternatively be used.