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- Muffin-tin_approximation abstract "The muffin-tin approximation is a shape approximation of the potential field in an atomistic environment. It is most commonly employed in quantum mechanical simulations of electronic band structure in solids. The approximation was proposed by John C. Slater. Augmented plane wave method is a method which uses muffin-tin approximation. It is a method to approximate the energy states of an electron in a crystal lattice. The basis approximation lies in the potential in which the potential is assumed to be spherically symmetric in the muffin-tin region and constant in the interstitial region. Wave functions (the augmented plane waves) are constructed by matching solutions of the Schrödinger equation within each sphere with plane-wave solutions in the interstitial region, and linear combinations of these wave functions are then determined by the variational method Many modern electronic structure methods employ the approximation. Among them are the augmented plane wave (APW) method, the linear muffin-tin orbital method (LMTO) and various Green's function methods. One application is found in the variational theory developed by Korringa (1947) and by Kohn and Rostoker (1954) referred to as the KKR method. This method has been adapted to treat random materials as well, where it is called the KKR coherent potential approximation.In its simplest form, non-overlapping spheres are centered on the atomic positions. Within these regions, the screened potential experienced by an electron is approximated to be spherically symmetric about the given nucleus. In the remaining interstitial region, the potential is approximated as a constant. Continuity of the potential between the atom-centered spheres and interstitial region is enforced.In the interstitial region of constant potential, the single electron wave functions can be expanded in terms of plane waves. In the atom-centered regions, the wave functions can be expanded in terms of spherical harmonics and the eigenfunctions of a radial Schrödinger equation. Such use of functions other than plane waves as basis functions is termed the augmented plane-wave approach (of which there are many variations). It allows for an efficient representation of single-particle wave functions in the vicinity of the atomic cores where they can vary rapidly (and where plane waves would be a poor choice on convergence grounds in the absence of a pseudopotential).".
- Muffin-tin_approximation wikiPageID "19127190".
- Muffin-tin_approximation wikiPageLength "6062".
- Muffin-tin_approximation wikiPageOutDegree "25".
- Muffin-tin_approximation wikiPageRevisionID "702652221".
- Muffin-tin_approximation wikiPageWikiLink Andersons_rule.
- Muffin-tin_approximation wikiPageWikiLink Band_gap.
- Muffin-tin_approximation wikiPageWikiLink Bloch_wave.
- Muffin-tin_approximation wikiPageWikiLink Category:Computational_physics.
- Muffin-tin_approximation wikiPageWikiLink Category:Condensed_matter_physics.
- Muffin-tin_approximation wikiPageWikiLink Category:Electronic_band_structures.
- Muffin-tin_approximation wikiPageWikiLink Category:Electronic_structure_methods.
- Muffin-tin_approximation wikiPageWikiLink Coherent_potential_approximation.
- Muffin-tin_approximation wikiPageWikiLink Eigenfunction.
- Muffin-tin_approximation wikiPageWikiLink Electronic_band_structure.
- Muffin-tin_approximation wikiPageWikiLink John_C._Slater.
- Muffin-tin_approximation wikiPageWikiLink Kohn–Sham_equations.
- Muffin-tin_approximation wikiPageWikiLink Korringa–Kohn–Rostoker_approximation.
- Muffin-tin_approximation wikiPageWikiLink Local-density_approximation.
- Muffin-tin_approximation wikiPageWikiLink Muffin_tin.
- Muffin-tin_approximation wikiPageWikiLink Particle_in_a_one-dimensional_lattice.
- Muffin-tin_approximation wikiPageWikiLink Plane_wave.
- Muffin-tin_approximation wikiPageWikiLink Potential.
- Muffin-tin_approximation wikiPageWikiLink Pseudopotential.
- Muffin-tin_approximation wikiPageWikiLink Quantum_mechanics.
- Muffin-tin_approximation wikiPageWikiLink Schrödinger_equation.
- Muffin-tin_approximation wikiPageWikiLink Screening_effect.
- Muffin-tin_approximation wikiPageWikiLink Solid-state_physics.
- Muffin-tin_approximation wikiPageWikiLink Spherical_harmonics.
- Muffin-tin_approximation wikiPageWikiLink Walter_Kohn.
- Muffin-tin_approximation wikiPageWikiLinkText "KKR method".
- Muffin-tin_approximation wikiPageWikiLinkText "LAPW".
- Muffin-tin_approximation wikiPageWikiLinkText "Muffin-tin approximation".
- Muffin-tin_approximation wikiPageWikiLinkText "exact muffin-tin orbital".
- Muffin-tin_approximation wikiPageWikiLinkText "linear augmented-plane-wave methods".
- Muffin-tin_approximation wikiPageWikiLinkText "muffin-tin approximation".
- Muffin-tin_approximation wikiPageUsesTemplate Template:Electronic_structure_methods.
- Muffin-tin_approximation wikiPageUsesTemplate Template:Reflist.
- Muffin-tin_approximation subject Category:Computational_physics.
- Muffin-tin_approximation subject Category:Condensed_matter_physics.
- Muffin-tin_approximation subject Category:Electronic_band_structures.
- Muffin-tin_approximation subject Category:Electronic_structure_methods.
- Muffin-tin_approximation hypernym Approximation.
- Muffin-tin_approximation type Area.
- Muffin-tin_approximation type Election.
- Muffin-tin_approximation type Area.
- Muffin-tin_approximation type Mechanic.
- Muffin-tin_approximation type Method.
- Muffin-tin_approximation type Physic.
- Muffin-tin_approximation comment "The muffin-tin approximation is a shape approximation of the potential field in an atomistic environment. It is most commonly employed in quantum mechanical simulations of electronic band structure in solids. The approximation was proposed by John C. Slater. Augmented plane wave method is a method which uses muffin-tin approximation. It is a method to approximate the energy states of an electron in a crystal lattice.".
- Muffin-tin_approximation label "Muffin-tin approximation".
- Muffin-tin_approximation sameAs Q6932011.
- Muffin-tin_approximation sameAs マフィンティンポテンシャル.
- Muffin-tin_approximation sameAs m.04jnhzp.
- Muffin-tin_approximation sameAs Q6932011.
- Muffin-tin_approximation wasDerivedFrom Muffin-tin_approximation?oldid=702652221.
- Muffin-tin_approximation isPrimaryTopicOf Muffin-tin_approximation.