- #1
Abdul.119
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Homework Statement
The (classical) energy of one-dimensional linear oscillator is
a) show, using the uncertainty relation, that the energy can be written as
b) Show that the minimum energy of the oscillator is
Where
Homework Equations
Δp Δx >= ħ/2
p ≈ ħ/2x
The Attempt at a Solution
I'm really stuck on this problem, I could say that the p_x = ħ^2 / (2x)^2 then substitute in the equation, but still where did the π and the 32 come from? I couldn't find any other relevant equations
Edit: Oh I just realized ħ = h/2π , then p^2 = h^2/(4πx)^2 , substituting in the equation would give the answer.
But now what about b)? I believe to find the minimum energy we set Δx >= ħ/2Δp , but it isn't clear to me how the frequency and angular velocity come in
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