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<math>\left\langle x^\prime|x^{\prime\prime}\right\rangle = \delta\left(x^\prime-x^{\prime\prime}\right)</math>
<math>\left\langle x^\prime|x^{\prime\prime}\right\rangle = \delta\left(x^\prime-x^{\prime\prime}\right)</math>
This relation should be thought of as a strictly canonical for use in integration, since writing the Dirac Delta Function in the absence of an integral is somewhat dubious. However, this does allow us to consider [[wavefunctions]] in terms of the Dirac Notation. Referring to the article on the [[Dirac Delta Function]], we see that:
<math>\left\langle x|\psi\right\rangle = \int\delta\left(x^\prime-x\right)\psi\left(x^\prime\right)dx^\prime</math>
And thus that the wavefunction in position space for a state <math>\left|\psi\right\rangle</math> can be written as:
<math>\psi\left(x\right)=\left\langle x|\psi\right\rangle</math>