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I have one question regarding the Kronecker delta and the Dirac notation. Is it possible to write
$\vert\phi_{m}\rangle\delta_{nq}\langle\phi_{p}\vert=\delta_{nq}\vert\phi_{m}\rangle\langle\phi_{p}\vert$
where $\vert\phi_{n}\rangle$ form an orthonormal basis?
Bra's, $\langle\,\cdot\,|$ and ket's $|\,\cdot\,\rangle$ are to be tought as simply vectors, like $\vec{v}^T$ and $\vec{v}$ respectively. These as you might already have learned are objects that live in a vector space and therefore enjoy all properties that have to do with linearity. The Kronecker symbol represents a number (scalar), indices in this context you can think of them as an identifier nothing more. So we know from linear algebra scalars commute with vectors, you can put them to the left or to the right without introducing any commutator.
