5.5.4.2 Solution complexsb-b

**Question:**

A more concise way of understanding the orthonormality of the two-particle spin states is to note that an inner product like

To check this argument, write out the sums over

The underlying mathematical principle is that sums of products can be factored into separate sums as in:

This is similar to the observation in calculus that integrals of products can be factored into separate integrals:

**Answer:**

and written out

and multiplying out, and reordering the second and third factor in each term, you see it is the same as the expression obtained in the answer to the previous question,