# Plot with manipulate

I want to use appropriately use the Manipulate command in conjunction with Plot, to construct animated graphics for the evolution of the solution. I have tried but i could not succed to solve it

$$f(x)=y_1(x)+0.2y_4(x)+0.01y_6(x)$$.

$$y_n$$ are the Eigenfunctions that defined as $$y_n(x)=\exp\left(\displaystyle{\frac{-x^2}{2}}\right)H_n(x)$$


Her[n_] := HermiteH[n, x]
Y[n_] := Exp[-x^2/2]*Her[n]
Y[1]
Y[4]
Y[6]
f[x_] = Y[1] + 0.2 Y[4] + 0.01 Y[6]
$$$$

• Your function eigen[n_] is not used anywhere? So why is it there? Mar 19, 2023 at 17:49
• I have changed it. I have only defined the eigenvalues Mar 19, 2023 at 17:55
• Your $f(x)$ is fixed. So it does not change? But you can see how $y_n(x)$ changes with $n$ as shown below. Otherwise you need to clarify how $f(x)$ changes. Mar 19, 2023 at 18:02

I assume you want to plot $$y_n(x)$$ as your $$f(x)$$ does not change? It is always better to pass all the parameters along to all the functions, (i.e. $$n,x$$) in this example. Do not pass somethings, say $$n$$, and leave others global (say $$x$$). This is a recipe for bugs when your program gets larger.

her[x_Symbol, n_Integer] := HermiteH[n, x]
Y[x_Symbol, n_Integer] := Exp[-x^2/2]*her[x, n]
f[x_Symbol, n_Integer] := Y[x, 1] + 2/10* Y[x, 4] + 1/100* Y[x, 6];
Manipulate[
Module[{x},
Plot[Evaluate@Y[x, n], {x, 0, 5},
PlotRange -> {Automatic, {-30, 30}}, PlotLabel -> Row[{" Y_", n }],
PlotStyle -> Red, GridLines -> Automatic,
GridLinesStyle -> LightGray]
],
{{n, 0, "n"}, 0, 5, 1, Appearance -> "Labeled"},
TrackedSymbols :> {n}
]
`