When to use Module inside Manipulate

*To*: mathgroup at smc.vnet.net*Subject*: [mg101025] When to use Module inside Manipulate*From*: Porscha Louise McRobbie <pmcrobbi at umich.edu>*Date*: Sun, 21 Jun 2009 07:05:59 -0400 (EDT)

Hello, I have defined a 2D complex function, and made side-by-side animations of the Re/Im parts inside a Manipulate. As written, I have the function definition as well as the animation wrapped in Module, and the animation/manipulate commands work fine (albeit slowly). However, if I remove that Module (it seems redundant to me), leaving only the outer DynamicModule, the cell where the graphs appear is highlighted, and the animate/manipulate no longer work. Any ideas about what I'm doing wrong? I suspect I'm not understanding how to localize variables properly. Thanks in advance, Porscha DynamicModule[{amp, phase, a, b}, Manipulate[a = 1; b = 1; Module[{Psi, T}, Psi[x_, y_] = Sqrt[1 - amp^2] Exp[-I \[Pi]^2/2 (4/a^2 + 1/b^2) T] 2/ Sqrt[a b] Sin[(2 Pi x)/a] Sin[(Pi y)/b] + amp Exp[I phase] Exp[-I \[Pi]^2/2 (9/a^2 + 1/b^2) T] 2/ Sqrt[a b] Sin[(3 Pi x)/a] Sin[(Pi y)/b] ; Animate[ GraphicsRow[{Plot3D[Re[Psi[x, y] /. T -> t], {x, 0, 1}, {y, 0, 1}, PlotRange -> {{0, 1}, {0, 1}, {-3, 3}}, PerformanceGoal -> "Quality", ColorFunction -> "Rainbow", Mesh -> None], Plot3D[Im[Psi[x, y] /. T -> t], {x, 0, 1}, {y, 0, 1}, PlotRange -> {{0, 1}, {0, 1}, {-3, 3}}, ColorFunction -> "Rainbow", PerformanceGoal -> "Quality", Mesh -> None]}, ImageSize -> 600], {t, 0.001, 5}, AnimationRunning -> False, AnimationRate -> .05]], {{amp, 0.5}, 0, 1, Appearance -> "Labeled", ImageSize -> Small}, {phase, 0, 2 Pi, Appearance -> "Labeled", ImageSize -> Small}, ControlPlacement -> Left, SaveDefinitions -> True]]

**Follow-Ups**:**Re: When to use Module inside Manipulate***From:*Porscha Louise McRobbie <pmcrobbi@umich.edu>

**Re: When to use Module inside Manipulate***From:*DrMajorBob <btreat1@austin.rr.com>