for de Broglie waves

& of wave number 1/2Δk
Modulation produce wave group
v p =
2
k 2
phase velocity
v g =Δω/Δk = dω/dk group velocity
for de Broglie waves
2mc
2
h
2
2
2m oc
2
h 1
v
c
(because hν=mc 2 )
2
2m
k
h
h
2m v
o
2
1
v
c
2
2
(because λ=h/mv)
* both ω&k are functions of body’s v v g = dω/dk =
d
dv
h
2m v
o
2
2
1
v 3 2
c
,
dk
dv
h
2m
3
2
1
v 2 2
v g = v (de Broglie group velocity)
o
c
d
dv
dk
dv
De Broglie wave group associated with a moving body travels
with the same velocity as the body.
De Broglie phase velocity v p =ω/k=c 2 /v
v p > velocity of the body v > c
(∵ it is not the motion of the body)
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