How to change a previous manipulate to include a condition for even and odd

Question

I have this manipulate

Manipulate[
 If[filllower > fillupper, filllower = fillupper]; 
 Grid[{{Show[
     Plot[(Sqrt[2] Sin[n \[Pi] x])^2, {x, 0, 1}, 
      PlotRange -> {{0, 1}, {0, 2}}], 
     If[filllower == fillupper, 
      Plot[(Sqrt[2] Sin[n \[Pi] x])^2, {x, 0, 1}, 
       PlotRange -> {{0, 1}, {0, 2}}], 
      Plot[(Sqrt[2] Sin[n \[Pi] x])^2, {x, filllower, fillupper}, 
       Filling -> 0, PlotRange -> {{0, 1}, {0, 2}}]], 
     AxesLabel -> {"x", "probability density"}, ImageSize -> 500, 
     AspectRatio -> .25, 
     PlotLabel -> 
      Grid[{{Row[{Style[
            "probability = " <> 
             ToString[
              NumberForm[
               Abs[Integrate[(Sqrt[2] Sin[n \[Pi] x])^2, {x, 
                  filllower, fillupper}]], {4, 3}, 
               NumberPadding -> {"", "0"}, 
               ExponentFunction -> (Null &)]], "Label"], 
           Style["  |  ", GrayLevel[.5]], 
           Style["quantum number = " <> ToString[n], "Label"]}]}}], 
     ImagePadding -> {{50, 50}, {30, 50}}]}, {Plot[(Sqrt[2] Sin[
        n \[Pi] x]), {x, 0, 1}, Frame -> True, ImageSize -> 500, 
     PlotRange -> {-Sqrt[2], Sqrt[2]}, 
     PlotLabel -> Style["wave function of the electron", "Label"], 
     AspectRatio -> .3, ImagePadding -> {{50, 50}, {50, 30}}]}}], 
 "X3" -> {{n, 1, "quantum number"}, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, 
   ControlType -> SetterBar}, 
 "X" -> {{filllower, 0, "lower limit"}, 0, 1, Appearance -> "Labeled"},
 "Y" -> {{fillupper, 1, "upper limit"}, 0, 1, 
   Appearance -> "Labeled"}]

but i want to have a condition ... for n odd ( 2 4 6 8 10, continuous this way ...

but for n even ( 1 3 5 7 ), changes all sin by cos - this is the only change .. and the same plot ... so for n odd, continuous sin and sin^2 , and for n even, change sen by cos and cos^2 ... how can i do that ? and if its possibles, up to the plots , in the manipulate, show the expression and show modifyng the n value.

Answer 1

I'm not completely sure I understand what you seek. Does this work?

Manipulate[If[filllower > fillupper, filllower = fillupper];
 With[{f = If[EvenQ@n, Sin, Cos]},
  Grid[{{Show[
      Plot[(Sqrt[2] f[n \[Pi] x])^2, {x, 0, 1}, 
       PlotRange -> {{0, 1}, {0, 2}}], 
      If[filllower == fillupper, 
       Plot[(Sqrt[2] f[n \[Pi] x])^2, {x, 0, 1}, 
        PlotRange -> {{0, 1}, {0, 2}}], 
       Plot[(Sqrt[2] f[n \[Pi] x])^2, {x, filllower, fillupper}, 
        Filling -> 0, PlotRange -> {{0, 1}, {0, 2}}]], 
      AxesLabel -> {"x", "probability density"}, ImageSize -> 500, 
      AspectRatio -> .25, 
      PlotLabel -> 
       Grid[{{Row[{Style[
             "probability = " <> 
              ToString[
               NumberForm[
                Abs[Integrate[(Sqrt[2] f[n \[Pi] x])^2, {x, filllower,
                    fillupper}]], {4, 3}, NumberPadding -> {"", "0"}, 
                ExponentFunction -> (Null &)]], "Label"], 
            Style["  |  ", GrayLevel[.5]], 
            Style["quantum number = " <> ToString[n], "Label"]}]}}], 
      ImagePadding -> {{50, 50}, {30, 50}}]}, {Plot[(Sqrt[2] f[
         n \[Pi] x]), {x, 0, 1}, Frame -> True, ImageSize -> 500, 
      PlotRange -> {-Sqrt[2], Sqrt[2]}, 
      PlotLabel -> Style["wave function of the electron", "Label"], 
      AspectRatio -> .3, ImagePadding -> {{50, 50}, {50, 30}}]}}]
  ], 
 "X3" -> {{n, 1, "quantum number"}, {1, 2, 3, 4, 5, 6, 7, 8, 9, 
    10}, ControlType -> SetterBar}, 
 "X" -> {{filllower, 0, "lower limit"}, 0, 1, 
   Appearance -> "Labeled"}, 
 "Y" -> {{fillupper, 1, "upper limit"}, 0, 1, 
   Appearance -> "Labeled"}]