- #1

mihailo

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## Homework Statement

The wave function is given as Ψ(x,t) = Ae^[i(k1x-ω1t)] + Ae^[i(k2x-ω2t)].

Show that particle average velocity Vav = ħ(k1+k2)/2m equals ω2-ω1/k2-k1.

Average momentum of the particle is Pav = ħ(k2+k1)/2.

## Homework Equations

p = ħk

E=ħω

K = 1/2 * mV^2

## The Attempt at a Solution

if we calculate |Ψ(x,t)|^2 = 2*A(1+cos((k2-k1)x-(ω2-ω1)t)) form V=ω/k we get ω2-ω1/k2-k1.

if we use average momentum Vav = Pav/m we get Vav = ħ(k1+k2)/2m.

my problem is to get mathematically form ħ(k1+k2)/2m to ω2-ω1/k2-k1