Position eigenstate
= Position eigenstate
{title2=$\widehat q|q\rangle=q|q\rangle$}
A generalized eigenstate of the <position operator> is labeled by its position eigenvalue. In a continuous <position> coordinate the normalization is distributional: $\langle q|q'\rangle=\delta(q-q')$ and $\int dq\,|q\rangle\langle q|=1$. Individual position eigenstates are not normalizable Hilbert-space vectors. The <Dirac delta distribution> normalization makes $\langle q_f|U|q_i\rangle$ the integral kernel of a <time-evolution operator>, such as the <free-particle propagator>.