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Quantum Mechanics with Basic Field Theory by Bipin R. Desai

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28 Addition of angular momenta

In the chapter on rotation we discussed methods for obtaining the eigenvalues and eigenstates of the operator related to angular momentum. These obviously refer to single-particle states. However, often one has a more complex system containing two or more particles, as happens for two-electron systems, the electron-proton state of the atom, or many-nucleon systems in nuclei. In this chapter we tackle some of these problems involving addition of angular momenta.

28.1 Combining eigenstates: simple examples

 

Let us consider the problem of expressing the product of two states |j1,m1〉, |j2, m2〉 in terms of a state that is an eigenstate of J2 and Jz, where

The operators J1 and J2 commute since they operate on different ...

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