If I have a general (not a plain wave) state $$|\psi\rangle$$, then in position space :(adsbygoogle = window.adsbygoogle || []).push({});

$$\langle \psi|\psi\rangle = \int^{\infty}_{-\infty}\psi^*(x)\psi(x)dx$$

is the total probability (total absolute, assuming the wave function is normalized)

So if the above is correct, does that mean

$$\langle x|x' \rangle= \delta(x-x')$$

is also the total probability ?

if that is the case, then the total probability is infinite! is that why plane waves are called unphysical? or is there more to it ?

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# I Meaning of Dirac Delta function in Quantum Mechanics

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