Angular Momentum Operator - Angular Momentum Coupling

Angular Momentum Coupling

Often, two or more sorts of angular momentum interact with each other, so that angular momentum can transfer from one to the other. For example, in spin-orbit coupling, angular momentum can transfer between L and S, but only the total J=L+S is conserved. In another example, in an atom with two electrons, each has its own angular momentum J₁ and J₂, but only the total J=J₁+J₂ is conserved.

In these situations, it is often useful to know the relationship between, on the one hand, states where all have definite values, and on the other hand, states where all have definite values, as the latter four are usually conserved (constants of motion). The procedure to go back and forth between these bases is to use Clebsch–Gordan coefficients.

One important result in this field is that is a relationship between the quantum numbers for :

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For an atom or molecule with J=L+S, the term symbol gives the quantum numbers associated with the operators .