# Heisenberg uncertainty for the harmonic oscillator?

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 I have to do a program about the Heisenberg uncertainty for the harmonic oscillator. I wrote all the integrals that I need to use for the medium values and the specific function of the oscillator, but it doesn't work...Could someone help me please? ψ[n_, x_] := Sqrt[α/(2^n n! Sqrt[π])] HermiteH[n, α x ] E^(-((α x)^2/2)) /. α -> 1; mediex[i_, x_] := \!$$\*SubsuperscriptBox[\(∫$$, $$0$$, $$∞$$]$$\((Abs[\ψ[i, x]])$$^2*x \[DifferentialD]x\)\) mediex[5, x]  15/(8 Sqrt[π]) mediex2[i_, x_] := \!$$\*SubsuperscriptBox[\(∫$$, $$0$$, $$∞$$]$$\((Abs[\ψ[i, x]])$$^2*x^2 \[DifferentialD]x\)\) mediex2[5, x]  11/4 mediep[i_, x_] := \!$$\*SubsuperscriptBox[\(∫$$, $$0$$, $$∞$$]$$ψ[i, x]*\((\(-iℏ$$\ )\) D[ψ[i, x], x] \[DifferentialD]x\)\) mediep[5, x]  0 mediep2[i_, x_] := \!$$\*SubsuperscriptBox[\(∫$$, $$0$$, $$∞$$]$$ψ[i, x]*\((ℏ^2\ )$$ D[D[ψ[i, x], x], x] \[DifferentialD]x\)\) mediep2[5, x]  -((11 ℏ^2)/4)
 I am by no means sure, but I think you should write mediep2[i_, x_] := -\!$$\*SubsuperscriptBox[\(\[Integral]$$, $$0$$, $$\[Infinity]$$]$$\[Psi][ i, x]*\((\[HBar]^2\ )$$ D[D[\[Psi][i, x], x], x] \[DifferentialD]x\)\) and then deltax[i_, x_] := Sqrt[mediex2[i, x] - mediex[i, x]^2] deltap[i_, x_] := Sqrt[mediep2[5, x] - (mediep[5, x])^2] and relatie[5, x] // PowerExpand // FullSimplify % // N