Consider a system of two particles with spin quantum numbers 1andS2respectivelyand with no orbital angular momentum. We have seen in class that this state can be described equally well in two different bases:

The Clebsh-Gordan Coefficients to relate the coupled and uncoupled bases.

Explanation:

In quantum mechanics, two different sources of angular momentum eigenstates, show their widening through the Clebsch–Gordan (CG) coefficients, first in an uncoupled product bases.

- The uncoupled basis writes the state as eigenstates of the z-components of    the two particles:

                               IS1+S2ms1ms2)

- The coupled basis writes the state as eigenstates of the two particles:

                                IS1S2Stotms)

this would be about 43%