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Quantum mechanics

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    Show that the plane waves  e^{ikx} are non-normalisable energy eigenstates for the free particle( i.e.  V(x)=0, \forall  x ). What does it mean for it to be a non-normalisable energy eigenstate? In the answer it says that the energy  E= \dfrac{\hbar k^2}{2m} but I'm not sure I understand why this shows it's non-normalisable.
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    (Original post by JBKProductions)
    Show that the plane waves  e^{ikx} are non-normalisable energy eigenstates for the free particle( i.e.  V(x)=0, \forall  x ). What does it mean for it to be a non-normalisable energy eigenstate? In the answer it says that the energy  E= \dfrac{\hbar k^2}{2m} but I'm not sure I understand why this shows it's non-normalisable.
    broadly speaking, a non normalisable eigenstate is one where, if you integrate the mod square of it's wavefunction over R^3, you get infinity.
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    Thanks.
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    F=Ma
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    (Original post by Jed_)
    F=Ma
    I think you mean:
    \frac{d}{dt}\hat{p}=-<\frac{dV}{d \hat{x}}>
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    (Original post by ben-smith)
    I think you mean:
    \frac{d}{dt}\hat{p}=-<\frac{dV}{d \hat{x}}>
    no my friend, you are mistaken the equation the you just said is Distance/time= speed. don't worry I am very experience in the field of mathematics so I can provide more assistance if you need it, this will lead to less embarrassing situations on your part.

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