Klein Gordon Field

Hi everyone! Im' a new member and I'm studying Quantum Field Theory.



I read this:



"The interpretation of the real scalar field is that it creates a particle (boson) with momentum p at the point x."



and :



[itex]\phi[/itex][itex]\left(x\right)[/itex] [itex]\left|0\right\rangle[/itex] = [itex]\int \frac{d^3p}{(2\pi)^3(2\varpi_p)}[/itex] [itex]e^{-ipx} |p\rangle[/itex] (1)



but I didn't understand this equality... i know that:



[itex]\phi (x) = \int \frac{d^3p}{(2\pi)^3(2\varpi_p)} (a_p e^{ipx} + a^+_p e^{-ipx})[/itex] (2)



So... where it goes the term [itex]a_p e^{ipx}[/itex] in the expression (1) ???



Can someone kindly show me all the steps?

I know it's a stupid question, but I can not understand.



thank you very much!!!!!