The following textbook Heisenberg's Quantum Mechanics shows an example of calculating Berry's curvature (top page on pg 518). It led to a following equation
[1] $$ V_{m} = {- 1 \over B^2 } * i * \sum { (<m,B|S|n,B> ∧ <n,B|S|m,B>) \over A^2} $$
the textbook claims that we add the term m = n since $$ <m|S|m> ∧ <m|S|m> = 0 $$ then the above equation simplifies to
[2] $$ V_{m} = {- 1 \over B^2 } * i * \sum { (<m,B|S ∧ S|m,B>) \over A^2} $$
The symbol ∧ stands for 'and' in logic or cross product in mathematics.
My question is how the author derived that claim and how it led to that equation [2] from equation [1] ?
My reasoning is that $$ |n,B> ∧ <n,B| = 1$$
because both are true. Furthermore 1 = 1 ∧ 1 then it leads to equation [2]. However, I believe my reasoning is to weak or invalid and I wondered if there is a better alternative to explain author's claim. note that there is bra > and ket < notation used here. Thanks.