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If the wavenumber eigenstates are |k> and the position eigenstates are |x>, then my notes say we can write

|k>=∫

i.e express a wavenumber eigenstate in terms of a superposition of position eigenstates. Now they state that e

|k>=∫

_{-∞}^{∞}e_{k}(x)|x>dxi.e express a wavenumber eigenstate in terms of a superposition of position eigenstates. Now they state that e

_{k}(x)=e^{ikx}/√(2π). I don't understand how we can say that the e_{k}(x) has this form... Can anyone explain? Thanks :)
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