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Hi I'm trying to create a Manipulate[Plot[]] so that I can vary lambda in the below equation from 0 to 2 and see how it affects my plot. I'm getting stuck a couple steps before that though where I use NDEigensystem to solve a potential. It keeps giving the error,

Set::shape: Lists {vals,funs} and NDEigensystem[29.1667 (E^(-0.261861x) - 2E^(-0.130931x) + E^(-0.0872872x) * [Lambda]) * u[x]-u''[x]/2,u[x],{x,-29.1667 (25.9352 exp+6177.79 * [Lambda]),100},1,Method->{SpatialDiscretization->{FiniteElement,{MeshOptions->{<<1>>}}}}] are not the same shape.

Here is the code I'm using that's giving me the error:

V[x_] := 7/(48(.005)) (E^(-2[x]/7.637626158259733) - 
    2 E^(x/7.637626158259733) + [Lambda]*E^(-2/3 x/7.637626158259733))
[L] = -h^2*u''[x] + V[x]*u[x]; {vals, 
  funs} = NDEigensystem[[L], 
  u[x], {x, -29.166666666666668 (2.357747434867739*
       exp(11) + 6177.788320394612 * [Lambda]), 100}, 1, 
  Method -> {"SpatialDiscretization" -> {"FiniteElement", \
{"MeshOptions" -> {MaxCellMeasure -> 0.01}}}}];

And here is the follow-up code that I'm trying to use to plot it all:

In[42]:= vals

Out[42]= vals

Manipulate[Show[Plot[Evaluate[h*funs + vals], {[x], -10, 10}, 
   BaseStyle -> {FontWeight -> "Bold", FontSize -> 12}, 
   AxesLabel ->{"x","V(x)"}, PlotPoints->1000, PlotStyle->{Thickness[0.009]}],Plot[V[x],{x,0.5,60},BaseStyle->{FontWeight->"Bold",FontSize->12},AxesLabel->{"x","V_(x)"},PlotPoints->1000,PlotStyle->{Thickness[0.009]}],PlotRange->{{0.5,60},{0.4}},AxesOrigin->{-5,0},ImageSize->Medium],{Lambda,0,2}]

I also provided a screenshot of the code I am basing this off of which worked fine for me, I think it's just because of the constant lambda I now have? I am also assuming that this is the reason there's nothing showing up for my Manipulate[Plot[]] so ideally if we can fix this shape issue then everything else should be good...I hope.

Side note: I already defined h above the error-producing code (in the nice error-free code; see image) which is why it's not shown in the bad error code.

Thanks for any help!! Note: the top code is the code I'm basing this off of and the bottom code is my current code that's failing me. Code that works beautifully for same exact style of equation

Bad Code

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    $\begingroup$ There seem to be lots of erroneous square brackets in your code. Also exp(11) should be Exp[11] $\endgroup$
    – MelaGo
    Commented Nov 18, 2020 at 3:34
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    $\begingroup$ This [L] = -h^2*u''[x] + V[x]*u[x] is not valid syntax. Try L=... and use L and not [L] in NDEigenststem $\endgroup$
    – user21
    Commented Nov 18, 2020 at 8:05
  • $\begingroup$ Oh thank you for the Exp help, I always forget that! But it didn't fix the problem. I should mention, I think a lot of the weird formatting in my code above is due to the copy/paste mess ups. For example, the L is supposed to be a capital script L and when I copy/pasted it, it came out as [ScriptCapitalL] but I wanted to make it look nicer so I got rid of the ScriptCapital part and forgot about the square brackets. My real code looks like the new image I've inserted into the OP. I apologize for not noticing the mess-ups. $\endgroup$ Commented Nov 18, 2020 at 18:53

1 Answer 1

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This produces some plots, but it's not exactly what you're asking for. (I changed the interval for NDEigensystem to {x, -30, 30} to avoid crashing)

Clear[L, V]
h = 1/Sqrt[2];

V[x_, lambda_] := 
 7/(48 (.005)) (E^(-2 x/7.637626158259733) - 
    2 E^(x/7.637626158259733) + lambda*E^(-2/3 x/7.637626158259733))

L[lambda_] := -h^2*u''[x] + V[x, lambda]*u[x]

f[lambda_] := 
 NDEigensystem[L[lambda], u[x], {x, -30, 30}, 1, 
  Method -> {"SpatialDiscretization" -> {"FiniteElement", \
{"MeshOptions" -> {MaxCellMeasure -> 0.01}}}}]

Manipulate[
 {funs, vals} = f[lambda];
 Show[
  Plot[h*funs + vals, {x, -10, 10}, AxesLabel -> {"x", "V(x)"}, 
   PlotStyle -> Red, PlotPoints -> 1000],
  Plot[V[x, lambda], {x, 0.5, 60}, PlotStyle -> Blue, 
   PlotPoints -> 1000],
  PlotRange -> {{0, 10}, {-5, 10}}
  ],
 {lambda, 0.1, 2}]

enter image description here

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