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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

V_{m}= (- 1/B^{2}) * i *∑ ( <m,B|S|n,B> ∧ <n,B|S|m,B> ) / A^{2}................[1]

the textbook claims that we add the term m = n since <m|S|m> ∧ <m|S|m> = 0 then the above equation simplifies to

V_{m}= (- 1/B^{2}) * i * ∑( <m,B|S ∧ S|n,B> ) / A^{2}.................[2]

The symbol ∧ stands for 'and' in logic or cross product.

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> 'and' <n,B| are both true therefore ( |n,B> 'and' <n,B|) = 1 which is equal to 1 'and' 1 however I do not believe that my reasoning is a valid one. What is the alternative to this?

Thanks.

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# Berry's Curvature Equation cross product calculation

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