Angular momentum diagrams (quantum mechanics)

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.

The diagrammatic notation is a considerably large topic in its own right with a number of specialized features – this article introduces the very basics.

In diagram form this is a doubleheaded arrow, pointing in the opposite direction to the ket.

There is no difference between the forward-time and reversed-time states for the outer product contraction, so here they share the same diagram, represented as one line without direction, again labelled by j only and not m: The tensor product ⊗ of n states |j1, m1⟩, |j2, m2⟩, ... |jn, mn⟩ is written and in diagram form, each separate state leaves or enters a common vertex creating a "fan" of arrows - n lines attached to a single vertex.