How to define the following operator in Mathematica?
$$\hat{\nabla}^4=\left(\frac{\partial^2}{\partial\hat{r}^2}+\frac1{\hat{r}}\frac{\partial}{\partial\hat{r}}\right)^2$$
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2 Answers
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It should be this:
lap = D[#, {r, 2}] + 1/r D[#, r] &;
lapsquared = lap @* lap;
lapsquared[f[r]] // Simplify
Or using Laplacian to define lap
lap = Laplacian[#, {r, θ}, "Polar"] &;
answered Mar 23, 2020 at 6:29
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1$\begingroup$ Wow, never knew of
@*AKAComposition! $\endgroup$– RuslanCommented Mar 23, 2020 at 18:37 -
1$\begingroup$ @Ruslan It happens to be it :); also
/*forRightComposition. $\endgroup$ Commented Mar 24, 2020 at 1:25
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A simple answer:
operator[f_] := Nest[(D[#, {r, 2}] + 1/r D[#, r]) &, f, 2]
operator[f[r]]
answered Mar 31, 2020 at 4:38
A little mouse on the pampasA little mouse on the pampas
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(Laplacian[u[r], {r,theta}, "Polar"])^2$\endgroup$Laplacianrather than directive square. $\endgroup$