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- Prolate_spheroidal_coordinates abstract "Prolate spheroidal coordinates are a three-dimensional orthogonal coordinate system that results from rotating the two-dimensional elliptic coordinate system about the focal axis of the ellipse, i.e., the symmetry axis on which the foci are located. Rotation about the other axis produces oblate spheroidal coordinates. Prolate spheroidal coordinates can also be considered as a limiting case of ellipsoidal coordinates in which the two smallest principal axes are equal in length.Prolate spheroidal coordinates can be used to solve various partial differential equations in which the boundary conditions match its symmetry and shape, such as solving for a field produced by two centers, which are taken as the foci on the z-axis. One example is solving for the wavefunction of an electron moving in the electromagnetic field of two positively charged nuclei, as in the hydrogen molecular ion, H2+. Another example is solving for the electric field generated by two small electrode tips. Other limiting cases include areas generated by a line segment (μ=0) or a line with a missing segment (ν=0).".
- Prolate_spheroidal_coordinates thumbnail Prolate_spheroidal_coordinates.png?width=300.
- Prolate_spheroidal_coordinates wikiPageExternalLink ProlateSpheroidalCoordinates.html.
- Prolate_spheroidal_coordinates wikiPageID "5007518".
- Prolate_spheroidal_coordinates wikiPageLength "11340".
- Prolate_spheroidal_coordinates wikiPageOutDegree "34".
- Prolate_spheroidal_coordinates wikiPageRevisionID "620893595".
- Prolate_spheroidal_coordinates wikiPageWikiLink 1-to-1_mapping.
- Prolate_spheroidal_coordinates wikiPageWikiLink Atomic_nucleus.
- Prolate_spheroidal_coordinates wikiPageWikiLink Bijection.
- Prolate_spheroidal_coordinates wikiPageWikiLink Cartesian_coordinate_system.
- Prolate_spheroidal_coordinates wikiPageWikiLink Cartesian_coordinates.
- Prolate_spheroidal_coordinates wikiPageWikiLink Category:Coordinate_systems.
- Prolate_spheroidal_coordinates wikiPageWikiLink Colatitude.
- Prolate_spheroidal_coordinates wikiPageWikiLink Coordinate_system.
- Prolate_spheroidal_coordinates wikiPageWikiLink Course_of_Theoretical_Physics.
- Prolate_spheroidal_coordinates wikiPageWikiLink Dihydrogen_cation.
- Prolate_spheroidal_coordinates wikiPageWikiLink Electric_field.
- Prolate_spheroidal_coordinates wikiPageWikiLink Electrode.
- Prolate_spheroidal_coordinates wikiPageWikiLink Electromagnetic_field.
- Prolate_spheroidal_coordinates wikiPageWikiLink Electron.
- Prolate_spheroidal_coordinates wikiPageWikiLink Ellipse.
- Prolate_spheroidal_coordinates wikiPageWikiLink Ellipsoid.
- Prolate_spheroidal_coordinates wikiPageWikiLink Ellipsoidal_coordinates.
- Prolate_spheroidal_coordinates wikiPageWikiLink Elliptic_coordinate_system.
- Prolate_spheroidal_coordinates wikiPageWikiLink Elliptic_coordinates.
- Prolate_spheroidal_coordinates wikiPageWikiLink Hydrogen_molecular_ion.
- Prolate_spheroidal_coordinates wikiPageWikiLink Hyperboloid.
- Prolate_spheroidal_coordinates wikiPageWikiLink Latitude.
- Prolate_spheroidal_coordinates wikiPageWikiLink Limiting_case_(mathematics).
- Prolate_spheroidal_coordinates wikiPageWikiLink Oblate_spheroidal_coordinates.
- Prolate_spheroidal_coordinates wikiPageWikiLink Orthogonal_coordinates.
- Prolate_spheroidal_coordinates wikiPageWikiLink Partial_differential_equation.
- Prolate_spheroidal_coordinates wikiPageWikiLink Prolate.
- Prolate_spheroidal_coordinates wikiPageWikiLink Separation_of_variables.
- Prolate_spheroidal_coordinates wikiPageWikiLink Spherical_coordinate_system.
- Prolate_spheroidal_coordinates wikiPageWikiLink Spherical_coordinates.
- Prolate_spheroidal_coordinates wikiPageWikiLink Spheroid.
- Prolate_spheroidal_coordinates wikiPageWikiLink Spheroids.
- Prolate_spheroidal_coordinates wikiPageWikiLink Wave_function.
- Prolate_spheroidal_coordinates wikiPageWikiLink Wavefunction.
- Prolate_spheroidal_coordinates wikiPageWikiLink File:ProlateSpheroidCoord.png.
- Prolate_spheroidal_coordinates wikiPageWikiLink File:Prolate_spheroidal_coordinates.png.
- Prolate_spheroidal_coordinates wikiPageWikiLink File:Prolate_spheroidal_coordinates_degenerate.png.
- Prolate_spheroidal_coordinates wikiPageWikiLinkText "Prolate spheroidal coordinates".
- Prolate_spheroidal_coordinates wikiPageWikiLinkText "prolate spheroidal coordinates".
- Prolate_spheroidal_coordinates hasPhotoCollection Prolate_spheroidal_coordinates.
- Prolate_spheroidal_coordinates wikiPageUsesTemplate Template:Cite_book.
- Prolate_spheroidal_coordinates wikiPageUsesTemplate Template:Orthogonal_coordinate_systems.
- Prolate_spheroidal_coordinates wikiPageUsesTemplate Template:Reflist.
- Prolate_spheroidal_coordinates subject Category:Coordinate_systems.
- Prolate_spheroidal_coordinates hypernym Orthogonal.
- Prolate_spheroidal_coordinates comment "Prolate spheroidal coordinates are a three-dimensional orthogonal coordinate system that results from rotating the two-dimensional elliptic coordinate system about the focal axis of the ellipse, i.e., the symmetry axis on which the foci are located. Rotation about the other axis produces oblate spheroidal coordinates.".
- Prolate_spheroidal_coordinates label "Prolate spheroidal coordinates".
- Prolate_spheroidal_coordinates sameAs m.0czkln.
- Prolate_spheroidal_coordinates sameAs Издужени_сфероидни_координатни_систем.
- Prolate_spheroidal_coordinates sameAs Q7249552.
- Prolate_spheroidal_coordinates sameAs Q7249552.
- Prolate_spheroidal_coordinates sameAs 長球面坐標系.
- Prolate_spheroidal_coordinates wasDerivedFrom Prolate_spheroidal_coordinates?oldid=620893595.
- Prolate_spheroidal_coordinates depiction Prolate_spheroidal_coordinates.png.
- Prolate_spheroidal_coordinates isPrimaryTopicOf Prolate_spheroidal_coordinates.