problem with Graphics array --plots don't appear
- To: mathgroup at smc.vnet.net
- Subject: [mg121012] problem with Graphics array --plots don't appear
- From: raj kumar <rajesh7796gm at gmail.com>
- Date: Mon, 22 Aug 2011 06:03:37 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
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]