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Quantum mechanics

Show that the plane waves eikx e^{ikx} are non-normalisable energy eigenstates for the free particle( i.e. V(x)=0,∀x 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=ℏk22m E= \dfrac{\hbar k^2}{2m} but I'm not sure I understand why this shows it's non-normalisable.
Original post by JBKProductions
Show that the plane waves eikx e^{ikx} are non-normalisable energy eigenstates for the free particle( i.e. V(x)=0,∀x 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=ℏk22m 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.
Thanks.
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Avatar for Jed_
Jed_
7
F=Ma
Original post by Jed_
F=Ma


I think you mean:
ddtp^=−<dVdx^>\frac{d}{dt}\hat{p}=-<\frac{dV}{d \hat{x}}>
Reply 5
Avatar for Jed_
Jed_
7
Original post by ben-smith
I think you mean:
ddtp^=−<dVdx^>\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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