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## Main Question or Discussion Point

Gents pls help me on the below since im confused and getting frustrated

suppose QM system is characterized by this expression [tex] \int dp \ e^{-ipx} |p> [/tex]

So how do i interpret it - one the one hand since that expression is |x>, I guess I say that my system is in ket state |x> and the observable which describes this system (position in this case) has eigenvalue x. Briefly if thinking about particle I say this particle is at position x.

on the other hand it is a superposition of plane waves exp(-ipx) and superposition of some |p> ket states right? I can no attach these two ideas - on the one hand particle at position x, on the other hand superposition of plane waves (free particle which has any momentum SOMEWHERE in space)

And what additional role |p> play here? (except with exp(-ipx) it gives me |x> )

Any response much appreciated

suppose QM system is characterized by this expression [tex] \int dp \ e^{-ipx} |p> [/tex]

So how do i interpret it - one the one hand since that expression is |x>, I guess I say that my system is in ket state |x> and the observable which describes this system (position in this case) has eigenvalue x. Briefly if thinking about particle I say this particle is at position x.

on the other hand it is a superposition of plane waves exp(-ipx) and superposition of some |p> ket states right? I can no attach these two ideas - on the one hand particle at position x, on the other hand superposition of plane waves (free particle which has any momentum SOMEWHERE in space)

And what additional role |p> play here? (except with exp(-ipx) it gives me |x> )

Any response much appreciated