Re: problem with Graphics array --plots don't appear

• To: mathgroup at smc.vnet.net
• Subject: [mg121019] Re: problem with Graphics array --plots don't appear
• From: raj kumar <rajesh7796gm at gmail.com>
• Date: Tue, 23 Aug 2011 05:47:13 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <j2t9l4\$m0h\$1@smc.vnet.net>

```oops...forgot to provide the starting potential p[x_]:= x+ 8 EXP[-x^2]

On Aug 22, 6:05 pm, raj kumar <rajesh779... at gmail.com> wrote:
> hi mathematica experts,
> i have  come across a code to obtain the wave  functions and energies
> for bound states of the schroedinger equation. however, plots of the
> the eigen functions cannot be generated-see graphics array below.
> since i am a novice in mathematica, any advise will be most
> appreciated.here is that code......    thanks
>
> ShootBSWF2[pot_, m_, emin_, emax_, xmin_, xmax_,
>    xmatch_, opts___Rule] :=
>   Module[{\[Psi], x, y, x0, trial, eq, bc, bc1, bc2,
>     \[Psi]1, \[Psi]2, ratio, evalue, e, norm1, norm2,
>     norm, optsRoot, optsND, opts2},
>    optsRoot = Sequence @@ FilterRules[
>        Flatten[{opts}], Options[FindRoot]];
>     optsND = Sequence @@ FilterRules[
>        Flatten[{opts}], Options[NDSolve]];
>     eq[e_, x_, x0_] :=
>      {-(Derivative[2][y][x]/(2*m)) +
>         pot[x]*y[x] == e*y[x], y[x0] == 0,
>       Derivative[1][y][x0] == 1/10^6};
>     y1[e_, x_] := y[x] /. NDSolve[eq[e, x, xmin],
>         y, {x, xmin, xmatch}, optsND][[1]];
>     bc1[e_] := D[y1[e, x], x]/y1[e, x] /.
>       x -> xmatch; y2[e_, x_] :=
>      y[x] /. NDSolve[eq[e, x, xmax], y,
>         {x, xmax, xmatch}, optsND][[1]];
>     bc2[e_] := D[y2[e, x], x]/y2[e, x] /.
>       x -> xmatch; bc[(e_)?NumericQ] :=
>      bc1[e] - bc2[e]; evalue = If[emax == emin,
>       emin, e /. With[{opts2 = optsRoot},
>         FindRoot[bc[e], {e, emin, emax}, opts2]]];
>     \[Psi]1[x_] = y1[evalue, x]; \[Psi]2[x_] =
>      y2[evalue, x]; ratio = \[Psi]1[xmatch]/
>       \[Psi]2[xmatch]; norm1 = NIntegrate[\[Psi]1[x]^2,
>       {x, xmin, xmatch}]; norm2 =
>      NIntegrate[\[Psi]2[x]^2, {x, xmatch, xmax}];
>     norm = 1/Sqrt[norm1 + ratio^2*norm2];
>     \[Psi][x_] = If[x <= xmatch, norm*\[Psi]1[x],
>       norm*ratio*\[Psi]2[x]]; {energy -> evalue,
>      wavefunction -> (\[Psi][#1] & ),
>      normalization -> norm}]
>
> solutions = {ShootBSWF2[pot, 0.5, 3, 4, -5, 5,
>      0.5, MaxIterations -> 50], ShootBSWF2[pot,
>      0.5, 4.4, 4.5, -5, 5, 0.5, MaxIterations ->
>       50], ShootBSWF2[pot, 0.5, 6, 7, -5, 5, 0.5,
>      MaxIterations -> 50], ShootBSWF2[pot, 0.5, 8,
>      9, -5, 5, 0.5, MaxIterations -> 50]};
>
> plot1 = PlotBSWF[solutions[[1]], -5, 5,
>     PlotRange -> {All, {2.5, 5.5}},
>     DisplayFunction -> Identity];
> plot2 = PlotBSWF[solutions[[2]], -5, 5,
>     PlotRange -> {All, {2.5, 5.5}},
>     DisplayFunction -> Identity];
> plot3 = PlotBSWF[solutions[[3]], -5, 5,
>     PlotRange -> {All, {5.5, 7.5}},
>     DisplayFunction -> Identity];
>   plot4 = PlotBSWF[solutions[[4]], -5, 5,
>     PlotRange -> {All, {7.5, 9}},
>     DisplayFunction -> Identity];
> plots = {{plot1, plot2}, {plot3, plot4}};
>
> GraphicsArray[{{plot1, plot2}, {plot3, plot4}},
>   DisplayFunction -> \$DisplayFunction]

```

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