If a freely moving electron is localized in space to within ∆x0 of x0, its wave function can be described by a wave packet
where f(k) is peaked around a central value k0. Which of the following is most nearly the width of the peak in k?
A.
B.
C.
D.
E.
(GR9277 #27)
Solution:
In quantum mechanics, the momentum p = ħk and position x wave functions are Fourier transform pairs and the relation between p and x representations forms the Heisenberg uncertainty relation:
∆x∆k ≥ 1 → ∆k ≥ 1/∆x
Or, since k and x are fourier variables, their localization would vary inversely.
Answer: B
No comments :
Post a Comment