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- TL;DR Summary
- When expanding a ket as a sum of components and basis unit vectors, Why is the order of ket and corresponding vector component reversed when writing the vector component as an inner product under the summation?

Shankar Prin. of QM 2nd Ed (and others) introduce the inner product:

<i|V> = v

They expand the ket |V> as:

|V> = Σ v

|V> = Σ |i><i|V> ...(Shankar 1.3.5)

Why do they reverse the order of the component v

<i|V> = v

_{i}...(Shankar 1.3.4)They expand the ket |V> as:

|V> = Σ v

_{i}|i>|V> = Σ |i><i|V> ...(Shankar 1.3.5)

Why do they reverse the order of the component v

_{i}and the ket |i> when they write the former as the inner product <i|V>? It should not matter right? The reversal of order is almost as if it is to stress the appearance of the outer product |i><i|.