About: Spherical basis

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In pure and applied mathematics, particularly quantum mechanics and computer graphics and their applications, a spherical basis is the basis used to express spherical tensors. The spherical basis closely relates to the description of angular momentum in quantum mechanics and spherical harmonic functions. While spherical polar coordinates are one orthogonal coordinate system for expressing vectors and tensors using polar and azimuthal angles and radial distance, the spherical basis are constructed from the standard basis and use complex numbers.

Attributes	Values
rdf:type	Thing yago:WikicatTensors yago:Abstraction100002137 yago:Cognition100023271 yago:Concept105835747 yago:Content105809192 yago:Idea105833840 yago:PsychologicalFeature100023100 yago:Quantity105855125 yago:Tensor105864481 yago:Variable105857459
rdfs:label	球面テンソル (ja) Spherical basis (en)
rdfs:comment	In pure and applied mathematics, particularly quantum mechanics and computer graphics and their applications, a spherical basis is the basis used to express spherical tensors. The spherical basis closely relates to the description of angular momentum in quantum mechanics and spherical harmonic functions. While spherical polar coordinates are one orthogonal coordinate system for expressing vectors and tensors using polar and azimuthal angles and radial distance, the spherical basis are constructed from the standard basis and use complex numbers. (en) 球面テンソル（または球テンソル）とは、に対して角運動量行列と同様に変換されるテンソルである。さらに演算子である場合は球面テンソル演算子と呼ばれる。階数k の球面テンソルは、角運動量k の状態と同じく2k+1 個の成分から成りと書かれる。光子の放出・吸収のような角運動量が重要な役割を演じる現象を記述する際に用いられる。演算子を球面テンソルで表現すると、角運動量の固有状態の間の遷移は、ウィグナー＝エッカルトの定理を用いることにより、取り扱いが簡単になる。 (ja)
rdfs:seeAlso	Wigner D-matrix Change of basis
dcterms:subject	Quantum mechanics Condensed matter physics Image processing Linear algebra Spherical geometry Tensors
Wikipage page ID	39653582 (xsd:integer)
Wikipage revision ID	1053164234 (xsd:integer)
Link from a Wikipage to another Wikipage	Cartesian coordinate system Quantum mechanics Basis (linear algebra) Applied mathematics Unitary operator Positive definiteness Quantum mechanics Complex number Cross product SO(3) Norm (mathematics) Coordinate system Coordinate vector Orthogonal coordinates Orthogonality Lie algebra Complex conjugate Computer graphics Orthonormal basis Standard basis Condensed matter physics Wigner D-matrix Wigner–Eckart theorem 3D rotation group Image processing Linear algebra Euclidean space Spherical geometry Tensors Transformation matrix Dot product Spherical harmonics Imaginary unit Unit vector Unitary matrix Pure mathematics Inverse matrix Matrix transpose Wigner D matrix Hermitian conjugate Spherical polar coordinates
Link from a Wikipage to an external page	https://books.google.com/books%3Fid=mAr0uwfBLwIC&q=angular+momentum+operators+when+expressed+in+the+spherical+basis&pg=PA69
sameAs	Spherical basis Spherical basis Spherical basis Spherical basis Spherical basis
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has abstract	In pure and applied mathematics, particularly quantum mechanics and computer graphics and their applications, a spherical basis is the basis used to express spherical tensors. The spherical basis closely relates to the description of angular momentum in quantum mechanics and spherical harmonic functions. While spherical polar coordinates are one orthogonal coordinate system for expressing vectors and tensors using polar and azimuthal angles and radial distance, the spherical basis are constructed from the standard basis and use complex numbers. (en) 球面テンソル（または球テンソル）とは、に対して角運動量行列と同様に変換されるテンソルである。さらに演算子である場合は球面テンソル演算子と呼ばれる。階数k の球面テンソルは、角運動量k の状態と同じく2k+1 個の成分から成りと書かれる。光子の放出・吸収のような角運動量が重要な役割を演じる現象を記述する際に用いられる。演算子を球面テンソルで表現すると、角運動量の固有状態の間の遷移は、ウィグナー＝エッカルトの定理を用いることにより、取り扱いが簡単になる。 (ja)
prov:wasDerivedFrom	wikipedia-en:Spherical_basis?oldid=1053164234&ns=0
page length (characters) of wiki page	10380 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Spherical_basis
is rdfs:seeAlso of	Spherical harmonics
is Link from a Wikipage to another Wikipage of	Rotation operator (quantum mechanics) Clebsch–Gordan coefficients

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