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- In quantum mechanics and its applications to quantum many-particle systems, notably quantum chemistry, angular momentum diagrams, or more accurately from a mathematical viewpoint angular momentum graphs, are a diagrammatic method for representing angular momentum quantum states of a quantum system allowing calculations to be done symbolically. More specifically, the arrows encode angular momentum states in bra–ket notation and include the abstract nature of the state, such as tensor products and transformation rules. The notation parallels the idea of Penrose graphical notation and Feynman diagrams. The diagrams consist of arrows and vertices with quantum numbers as labels, hence the alternative term "graphs". The sense of each arrow is related to Hermitian conjugation, which roughly corresponds to time reversal of the angular momentum states (c.f. Schrödinger equation). The diagrammatic notation is a considerably large topic in its own right with a number of specialized features – this article introduces the very basics. They were developed primarily by Adolfas Jucys (sometimes translated as Yutsis) in the twentieth century. (en)
- 在量子力學以及其應用如多體問題、量子化學等領域中，角動量圖是一種圖形表示法，用以代表一量子系統的角動量量子態，使得相關計算能以符號形式推演。此方法的箭號將角動量態與狄拉克符號連結。 此方法是由立陶宛物理學家於20世紀發明。在量子力學以及量子場論領域中，形似的符號表示法尚有費曼圖與潘洛斯圖形符號。這些圖樣包含有箭頭與頂點，有些還有量子數的標記。 (zh)
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- Bra (en)
- Diagram for a 6-j symbol, . (en)
- Diagram for a 9-j symbol, . (en)
- Inner product of and , that is . Similarly for more than three pairs of angular momenta. (en)
- Inner product of and , that is . (en)
- Ket (en)
- Outer product of and , that is . (en)
- Time reversed bra . (en)
- Time reversed equivalent. (en)
- Time reversed ket . (en)
- Tensor product of , , , that is = . Similarly for more than three angular momenta. (en)
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- AM diagrams bra time reversed.svg (en)
- AM diagrams bra.svg (en)
- AM diagrams inner product of tensor product.svg (en)
- AM diagrams inner product time reversed.svg (en)
- AM diagrams inner product.svg (en)
- AM diagrams ket time reversed.svg (en)
- AM diagrams ket.svg (en)
- AM diagrams outer product time reversed.svg (en)
- AM diagrams outer product.svg (en)
- AM diagrams tensor product kets time reversed.svg (en)
- AM diagrams tensor product kets.svg (en)
- Jucys diagram for Wigner 6-j symbol.svg (en)
- Jucys diagram for Wigner 9-j symbol.svg (en)
- AM diagrams inner product of tensor product time reversed.svg (en)
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- 在量子力學以及其應用如多體問題、量子化學等領域中，角動量圖是一種圖形表示法，用以代表一量子系統的角動量量子態，使得相關計算能以符號形式推演。此方法的箭號將角動量態與狄拉克符號連結。 此方法是由立陶宛物理學家於20世紀發明。在量子力學以及量子場論領域中，形似的符號表示法尚有費曼圖與潘洛斯圖形符號。這些圖樣包含有箭頭與頂點，有些還有量子數的標記。 (zh)
- In quantum mechanics and its applications to quantum many-particle systems, notably quantum chemistry, angular momentum diagrams, or more accurately from a mathematical viewpoint angular momentum graphs, are a diagrammatic method for representing angular momentum quantum states of a quantum system allowing calculations to be done symbolically. More specifically, the arrows encode angular momentum states in bra–ket notation and include the abstract nature of the state, such as tensor products and transformation rules. (en)
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- Angular momentum diagrams (quantum mechanics) (en)
- 角動量圖 (zh)
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