(* Creating the HTML - for each example *) page := Module[ {dirhandle,ofile,mcol,mrow,mcollast,mc,nex,endpage,rpoints,mrpoints,r,sr,file1,file2,if1,if2}, If[!ifpage, Goto[endpage]]; If[Head[handle] =!= String, Print["Error: page: handle is not a string: ", handle]; Goto[endpage]]; dirhandle = ToFileName[{dirhtml,handle}]; If[FileType[dirhandle] =!= Directory, CreateDirectory[dirhandle]]; ofile = ToFileName[dirhandle, "index.htm"]; of = OpenWrite[ofile, FormatType -> OutputForm, PageWidth -> Infinity]; rpoints = {0, 1, 2, 5, 10, 15, 20}; rpoints = Table[n, {n, 0, 100}]; mrpoints = Length[rpoints]; " \n \n "<>name<>"\n \n \n \n \n

"<>name<>" w(r) = "<>wname<>"

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The potential (red line is the energy)

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Calculation of classical trajectories

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Plot of trajectories on the potential surface

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Mapping (y, t) –> (qx, qy)

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Zeroes of the Jacobian

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Left: red curves show the points where Jacobian of the transformation (y, t) –> (qx, qy) is zero.
Right: blue curves show the points where Jacobian of the transformation (y, t) –> (px, py) is zero. \n \n

Caustics

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The same as above, but mapped into (qx, qy) plane. \n

Exact calculations

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Phase shift vs. angular momentum for partial waves

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Density plots

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Absolute value of the wavefunction

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Real part of the wavefunction

\n \n Animation \n \n

Contour plots

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Absolute value of the wavefunction

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Grey area - |psi| < 1, white - 1 < |psi| < 2, red - |psi| > 2. \n \n

Real part of the wavefunction

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Pink - Re psi > 0, blue - Re psi < 0, darker - |Re psi| > 2. \n Animation \n

Semiclassical calculations

\n " // o; If[FileType[ToFileName[dirhandle, "ntraj.gif"]] === File, " \n

Number of contributing trajectories

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Dark area corresponds to one or no trajectories, lighter areas correspond to multiple trajectories. \n " // o]; " \n

Density plots

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Absolute value of the wavefunction

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Real part of the wavefunction

\n \n Animation \n \n

Contour plots

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Absolute value of the wavefunction

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Grey area - |psi| < 1, white - 1 < |psi| < 2, red - |psi| > 2. \n \n

Real part of the wavefunction

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Pink - Re psi > 0, blue - Re psi < 0, darker - |Re psi| > 2. \n Animation \n \n

Comparison of exact and semiclassical wavefunctions

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Absolute value. Left - exact, right - semiclassical

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Real part. Left - exact, right - semiclassical

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Animate
Animate
\n " // o; Do[ r = rpoints[[nrpoints]]; sr = ToString[r]; file1 = ToFileName[subdirhtml, "chi" <> sr <> ".gif"]; file2 = ToFileName[subdirhtml, "psi" <> sr <> ".gif"]; if1 = (FileType[file1] === File); if2 = (FileType[file2] === File); If[if1 || if2, ("

R = " <> sr <> "

\n \n ") // o; ]; If[if1, ("

Dependence of angle chi on angle phi for the given R = " <> sr <> "

\n \n sr <> ".gif\">\n " )// o; ]; If[if2, ("

Primitive semiclassical (black) vs. exact wavefunction (red curves) for the given R = " <> sr <> ".
Plots show absolute value, real part, and number of contributing trajectories as a function of x

\n \n sr <> ".gif\">\n " )// o; ]; ,{nrpoints, mrpoints}]; "
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More examples of potentials

\n " // o; mcol = 5; mrow = Ceiling[mexamp/mcol]; mcollast = mexamp - (mrow-1)mcol; Do[ "" // o; mc = If[nrow==mrow,mcollast,mcol]; Do[ nex=(nrow-1)mcol+nc; " If[nex==nexamp, " BGCOLOR=\"#FFFF00\"", ""] <> "> tabexamp[[nex+1,2]] <> "/index.htm\"> tabexamp[[nex+1,2]] <> "/pot.gif\" BORDER = \"0\" ALT=\"" <> tabexamp[[nex+1,3]] <> "\" TITLE=\"" <> tabexamp[[nex+1,3]] <> "\">" // o; , {nc,mc}]; "" // o; , {nrow, mrow}]; "
\n \n

Table of examples of two-dimensional potentials\n \n \n \n \n " // o; "" // o; Close[of]; Label[endpage]; ];