(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 4.0, MathReader 4.0, or any compatible application. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 15525, 513]*) (*NotebookOutlinePosition[ 50835, 1725]*) (* CellTagsIndexPosition[ 50791, 1721]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Particle in an Infinite Square Well", "Title"], Cell["S. M. Rochester and D. Budker; August 2000", "Text"], Cell[CellGroupData[{ Cell["Mathematica Setup", "Subtitle", InitializationCell->True], Cell["\<\ Some settings and graphics definitions used in the Mathematica notebook -- \ feel free to ignore this stuff\ \>", "Text", InitializationCell->True], Cell[BoxData[ \(Off[General::"\", FactorSquareFree::"\", PolynomialGCD::"\"]\)], "Input", InitializationCell->True], Cell[BoxData[ \(<< Graphics`FilledPlot`\)], "Input", InitializationCell->True], Cell[BoxData[ \(shadedRectangle[{x1_, y1_}, {x2_, y2_}, n_] := {Line[{{x1, y1}, {x1, y2}, {x2, y2}, {x2, y1}, {x1, y1}}], Table[Line[{{x1, y1 + i \((y2 - y1)\)/n}, {x2 - i \((x2 - x1)\)/n, y2}}], {i, 0, n}], Table[Line[{{x1 + i \((x2 - x1)\)/n, y1}, {x2, y2 - i \((y2 - y1)\)/n}}], {i, 1, n}]}\)], "Input", InitializationCell->True], Cell[BoxData[ \(shadedRectangle1[{x1_, y1_}, {x2_, y2_}, n_] := {Line[{{x1, y2}, {x1, y1}, {x2, y1}, {x2, y2}}], Table[Line[{{x1, y1 + i \((y2 - y1)\)/n}, {x2 - i \((x2 - x1)\)/n, y2}}], {i, 0, n}], Table[Line[{{x1 + i \((x2 - x1)\)/n, y1}, {x2, y2 - i \((y2 - y1)\)/n}}], {i, 1, n}]}\)], "Input", InitializationCell->True], Cell[BoxData[ \(\(SetOptions[ListPlot, ImageSize \[Rule] {8\ 72, Automatic}, TextStyle \[Rule] {FontSize \[Rule] 16, FontFamily \[Rule] "\"}, PlotRange \[Rule] All, Frame \[Rule] True, Axes \[Rule] {True, False}, PlotStyle \[Rule] {PointSize[ .015]}];\)\)], "Input", InitializationCell->True], Cell[BoxData[ \(ComplexConjugate[x_] := x /. \[ImaginaryI] \[Rule] \(-\[ImaginaryI]\)\)], "Input", InitializationCell->True], Cell[BoxData[ \(WellPlot[ P_] := \((plot = FilledPlot[P, {x, 0, a}, PlotRange \[Rule] {{0, a}, {0, 1}}, Fills \[Rule] {RGBColor[1, 0, 0]}, PlotPoints \[Rule] 151, Frame \[Rule] {True, False, False, False}, FrameLabel \[Rule] None, FrameTicks \[Rule] False, DisplayFunction \[Rule] Identity]; \[IndentingNewLine]Show[{FullGraphics[plot], Graphics[{shadedRectangle1[{a\ 1, 0}, {a\ 1.2, 2}, 10], shadedRectangle1[{\(- .2\)\ a, 0}, {0, 2}, 10]}]}, PlotRange \[Rule] {{\(- .2\)\ a, 1.2\ a}, {\(-2\), 2}}, ImageSize \[Rule] {4\ 72, Automatic}, TextStyle \[Rule] {FontSize \[Rule] 24, FontFamily \[Rule] "\"}, DisplayFunction \[Rule] $DisplayFunction])\)\)], "Input", InitializationCell->True], Cell[BoxData[ \(WellAnimate[P_, tmax_, nsteps_] := \((P1 = N[P]; expo = Floor[Log[10, tmax]]; Table[plot = FilledPlot[P1, {x, 0, a}, PlotRange \[Rule] {{0, a}, {0, 1}}, Fills \[Rule] {RGBColor[1, 0, 0]}, PlotPoints \[Rule] 151, Frame \[Rule] {True, False, False, False}, FrameLabel \[Rule] None, FrameTicks \[Rule] False, DisplayFunction \[Rule] Identity]; \[IndentingNewLine]Show[{FullGraphics[plot], Graphics[{shadedRectangle1[{a\ 1, 0}, {a\ 1.2, 2}, 10], shadedRectangle1[{\(- .2\)\ a, 0}, {0, 2}, 10]}]}, PlotRange \[Rule] {{\(- .2\)\ a, 1.2\ a}, {\(-2\), 2}}, ImageSize \[Rule] {4\ 72, Automatic}, TextStyle \[Rule] {FontSize \[Rule] 12, FontFamily \[Rule] "\"}, Epilog \[Rule] {Text[ SequenceForm["\", PaddedForm[t/10\^expo, {3, 2}], DisplayForm[ RowBox[{"\<\[Times]\>", SuperscriptBox["\<10\>", expo]}]], "\< sec\>"], Scaled[{ .4, .9}], {\(-1\), 0}]}, DisplayFunction \[Rule] $DisplayFunction], {t, 0. , tmax \((1 - 1/nsteps)\), tmax/nsteps}])\)\)], "Input", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell["Define the eigenstates", "Subtitle", InitializationCell->True], Cell[TextData[{ "These are the energy eigenvalues; ", Cell[BoxData[ \(TraditionalForm\`n\)]], " is the mode number, ", Cell[BoxData[ \(TraditionalForm\`a\)]], " is the size of the well, ", Cell[BoxData[ \(TraditionalForm\`m\)]], " is the mass." }], "Text", InitializationCell->True], Cell["\<\ Let's put in some values for an electron in a well of atomic proportions\ \>", "Text", InitializationCell->True], Cell[BoxData[ \(\(\(\[HBar] = \ 1.05\ 10\^\(-27\);\)\( (*erg\ s*) \)\)\)], "Input", InitializationCell->True], Cell[BoxData[ \(\(\(m = \ 0.91\ 10\^\(-27\);\)\( (*g*) \)\)\)], "Input", InitializationCell->True], Cell[BoxData[ \(\(\(a = \ 10\ 10\^\(-8\);\)\( (*cm*) \)\)\)], "Input", InitializationCell->True], Cell[BoxData[ \(\(En\_n_ = \(\(\[Pi]\^2\) \[HBar]\^2\)\/\(2\ m\ a\^2\)\ n\^2;\)\)], \ "Input", InitializationCell->True], Cell["\<\ These are the corresponding eigenfunctions, including the time dependence \ specified by the Schrodinger equation.\ \>", "Text", InitializationCell->True], Cell[BoxData[ \(\(\[Psi]\_n_[x_, t_] = \(\@\(2\/a\)\) Sin[\(n\ \[Pi]\ x\)\/a]\ \[ExponentialE]\^\(\(-\[ImaginaryI]\)\ \ En\_n\ t/\[HBar]\);\)\)], "Input", InitializationCell->True], Cell["\<\ The probability density is the square of the absolute value of the \ wavefunction\ \>", "Text", InitializationCell->True], Cell[BoxData[ \(\(P[\[Psi]_] = Abs[\[Psi]]\^2;\)\)], "Input", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell["Plot some eigenstates", "Subtitle"], Cell["\<\ Let's plot the amplitudes and probability density of some of these \ eigenfunctions.\ \>", "Text"], Cell[CellGroupData[{ Cell[" n=1", "Section"], Cell[BoxData[ \(\(WellPlot[\(\@\(a\/2\)\) \[Psi]\_1[x, 0]];\)\)], "Input"], Cell[BoxData[ \(\(WellPlot[\(a\/2\) P[\[Psi]\_1[x, 0]]];\)\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell[" n=2", "Section"], Cell[BoxData[ \(\(WellPlot[\(\@\(a\/2\)\) \[Psi]\_2[x, 0]];\)\)], "Input"], Cell[BoxData[ \(\(WellPlot[\(a\/2\) P[\[Psi]\_2[x, 0]]];\)\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell[" n=10", "Section"], Cell[BoxData[ \(\(WellPlot[\(\@\(a\/2\)\) \[Psi]\_10[x, 0]];\)\)], "Input"], Cell[BoxData[ \(\(WellPlot[\(a\/2\) P[\[Psi]\_10[x, 0]]];\)\)], "Input"], Cell[TextData[{ "Note that the number of zeros at points between the boundaries is ", Cell[BoxData[ \(TraditionalForm\`\((n - 1)\)\)]], ". There is a theorem that says that this should be the case for any \ potential well. (See e.g. Landau & Lifshitz)" }], "Text"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Superpositions of eigenstates", "Subtitle"], Cell["\<\ The wavefunctions above are eigenfunctions, so their probability density \ plots are independent of time. This is not the case for a superposition of \ eigenstates. \ \>", "Text"], Cell[CellGroupData[{ Cell[TextData[{ "Example 1: ", Cell[BoxData[ \(TraditionalForm\`\[Psi]\_1\)]], " + ", Cell[BoxData[ \(TraditionalForm\`\[Psi]\_2\)]] }], "Section"], Cell[TextData[{ "Here is the simplest case of a superposition of eigenstates--equal parts \ of ", Cell[BoxData[ \(TraditionalForm\`\[Psi]\_1\)]], " and ", Cell[BoxData[ \(TraditionalForm\`\[Psi]\_2\)]], "." }], "Text"], Cell[BoxData[ \(\(WellAnimate[\(a\/4\) P[\[Psi]\_1[x, t] + \[Psi]\_2[x, t]], \(1\/\(\(3\)\(\ \)\)\) \(2 \[Pi]\ \[HBar]\)\/En\_1, 50];\)\)], "Input"], Cell[TextData[{ StyleBox["Question:", FontWeight->"Bold", FontColor->RGBColor[0.996109, 0.500008, 0]], " Can you calculate the period of oscillation?" }], "Text", CellFrame->{{0, 0}, {2, 0}}, CellDingbat->None] }, Closed]], Cell[CellGroupData[{ Cell["Example 2: Gaussian wave packet", "Section"], Cell["\<\ It is intereresting to make a connection with the classical case.To do this, \ consider a Gaussian wave packet.\ \>", "Text"], Cell["\<\ We choose a Gaussian wave function because (1) It is localized in space (2) In free space, a Gaussian wave function travels without changing shape\ \>", "Text"], Cell[CellGroupData[{ Cell["Part 1:", "Subsection"], Cell[TextData[{ "This wavefunction, at ", Cell[BoxData[ \(TraditionalForm\`t = 0\)]], ", has width ", Cell[BoxData[ \(TraditionalForm\`1/10\)]], " (in units of ", Cell[BoxData[ \(TraditionalForm\`a\)]], ") and is localized at the center of the well." }], "Text"], Cell[BoxData[ \(\(G[x_, 0] = \[ExponentialE]\^\(-\((\(x - a/2\)\/\(a/10\))\)\^2\);\)\)], \ "Input"], Cell[TextData[{ "In order to calculate the dynamics, we need to write this wave function as \ a superposition ", Cell[BoxData[ \(TraditionalForm\`\[Sum]\(c\_n\) \[Psi]\_n\)]], " of eigenstates of the well. The coefficients ", Cell[BoxData[ \(TraditionalForm\`c\_n\)]], " are given by" }], "Text"], Cell[BoxData[ \(\(c\_n_ = \[Integral]\_0\%a G[x, 0] ComplexConjugate[\ \[Psi]\_n[x, 0]] \[DifferentialD]x;\)\)], "Input"], Cell["\<\ Here are the magnitudes of the first 25 coefficients--as we can see from the \ plot, 25 is all we need.\ \>", "Text"], Cell[BoxData[ \(\(ListPlot[Table[{n, Abs[c\_n]}, {n, 25}], FrameLabel \[Rule] {"\", \*"\"\<|\!\(c\_n\)|\>\""}];\)\)], "Input"], Cell[TextData[{ StyleBox["Question:", FontWeight->"Bold", FontColor->RGBColor[0.996109, 0.500008, 0]], StyleBox[" ", FontColor->RGBColor[0.996109, 0.500008, 0]], "Why is every other coefficient zero?" }], "Text", CellFrame->{{0, 0}, {2, 0}}], Cell["Thus, we can write", "Text"], Cell[BoxData[ \(\(G[x_, t_] = \[Sum]\+\(n = 1\)\%25 c\_n\ \[Psi]\_n[x, t];\)\)], "Input"], Cell[TextData[{ "Since we know the time dependencies of the ", Cell[BoxData[ \(TraditionalForm\`\[Psi]\_n\)]], ", we know the time dependence of ", Cell[BoxData[ \(TraditionalForm\`G\)]], ". \nCan you predict what will happen?" }], "Text"], Cell[BoxData[ \(\(WellAnimate[P[G[x, t]], \((1\/8)\) \(2 \[Pi]\ \[HBar]\)\/En\_1, 50];\)\)], "Input"], Cell[TextData[{ "The wave packet has no net momentum ", Cell[BoxData[ \(TraditionalForm\`p\)]], ", thus, the center of the wave packet does not move. However, since we \ know the approximate position of the packet at ", Cell[BoxData[ \(TraditionalForm\`t = 0\)]], ", by the uncertainty principle, there must be a spread ", Cell[BoxData[ \(TraditionalForm\`\((\[CapitalDelta]p\)\)]], ") in the momentum. Thus the packet spreads out, although it eventually \ reforms. (This is known in the lingo as \"collapse and revival.\")" }], "Text"], Cell[TextData[{ StyleBox["Question:", FontWeight->"Bold", FontColor->RGBColor[0.996109, 0.500008, 0]], StyleBox[" ", FontColor->RGBColor[0.996109, 0.500008, 0]], " What is the period of oscillation in this case?" }], "Text", CellFrame->{{0, 0}, {2, 0}}], Cell["\<\ For the wave packet to go somewhere, it needs to have intial momentum. Let's \ add some...\ \>", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Part 2:", "Subsection"], Cell[TextData[{ "We'll give the wave packet an initial \"kick\" of momentum ", Cell[BoxData[ \(TraditionalForm\`p\)]], "." }], "Text"], Cell[BoxData[ \(\(G[x_, 0, p_] = G[x, 0] \[ExponentialE]\^\(\[ImaginaryI]\ x\ p/\[HBar]\);\)\)], \ "Input"], Cell["We calculate the coefficients as before:", "Text"], Cell[BoxData[ \(\(c\_\(n_, p_\) = \[Integral]\_0\%a G[x, 0, p]\ ComplexConjugate[\[Psi]\_n[x, 0]] \[DifferentialD]x;\)\)], "Input"], Cell[BoxData[ \(\(ListPlot[ Table[{n, Abs[c\_\(n, 400\ \[HBar]\ \[Pi]/a\)]}, {n, 400 - 25, 400 + 25}], FrameLabel \[Rule] {"\", \*"\"\<|\!\(c\_n\)|\>\""}];\)\)], "Input"], Cell[TextData[{ StyleBox["Question:", FontWeight->"Bold", FontColor->RGBColor[0.996109, 0.500008, 0]], StyleBox[" ", FontColor->RGBColor[0.996109, 0.500008, 0]], " Explain why the magnitudes of the coefficients ", Cell[BoxData[ \(TraditionalForm\`c\_n\)]], " peak where they do? \n(Hint: using the eigenenergy ", Cell[BoxData[ \(TraditionalForm\`E\_n\)]], ", calculate a charactaristic momentum associated with this state)" }], "Text", CellFrame->{{0, 0}, {2, 0}}], Cell[BoxData[ \(\(G[x_, t_, p_] := \[Sum]\+\(n = p/\((\[HBar]\ \[Pi]/a)\) - 25\)\%\(p/\ \((\ \[HBar]\ \[Pi]/a)\) + 25\)c\_\(n, p\)\ \[Psi]\_n[x, t];\)\)], "Input"], Cell[TextData[{ "Now the particle bounces from wall to wall. We are plotting the motion \ over a much shorter time span than in Part 1. The momentum is so much larger \ than the uncertainty in momentum (", Cell[BoxData[ \(TraditionalForm\`p \[GreaterGreater] \[CapitalDelta]p\)]], ") that it barely spreads at all during the time it takes to traverse the \ well. Notice the interference of the reflected and incoming parts of the wave \ packet near the walls." }], "Text"], Cell[BoxData[ \(\(WellAnimate[P[G[x, t, 400\ \[HBar]\ \[Pi]/a]], 2 \((\(400\ \[HBar]\ \[Pi]\)\/\(a\^2\ m\))\)\^\(-1\), 50];\)\)], "Input"], Cell["Here's one with smaller momentum", "Text"], Cell[BoxData[ \(\(WellAnimate[P[G[x, t, 100\ \[HBar]\ \[Pi]/a]], 2 \((\(100\ \[HBar]\ \[Pi]\)\/\(a\^2\ m\))\)\^\(-1\), 50];\)\)], "Input"] }, Closed]] }, Closed]] }, Closed]] }, Open ]] }, FrontEndVersion->"4.0 for Microsoft Windows", ScreenRectangle->{{0, 1024}, {0, 695}}, AutoGeneratedPackage->None, WindowSize->{1016, 668}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, CellLabelAutoDelete->True, StyleDefinitions -> Notebook[{ Cell[CellGroupData[{ Cell["Style Definitions", "Subtitle"], Cell["\<\ Modify the definitions below to change the default appearance of all cells in \ a given style. 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"mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica"}, Hyphenation->True, LineSpacing->{1, 3}, CounterIncrements->"Text", FontSize->14], Cell[StyleData["Text", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, LineSpacing->{1, 5}, FontSize->16], Cell[StyleData["Text", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}, FontSize->11], Cell[StyleData["Text", "Printout"], CellMargins->{{2, 2}, {6, 6}}, TextJustification->0.5, FontSize->10] }, Open ]], Cell[CellGroupData[{ Cell[StyleData["SmallText"], CellMargins->{{12, 10}, {6, 6}}, DefaultNewInlineCellStyle->"None", Hyphenation->True, LineSpacing->{1, 3}, LanguageCategory->"NaturalLanguage", CounterIncrements->"SmallText", FontFamily->"Helvetica", FontSize->9], Cell[StyleData["SmallText", "Presentation"], CellMargins->{{24, 10}, {8, 8}}, LineSpacing->{1, 5}, FontSize->12], Cell[StyleData["SmallText", "Condensed"], CellMargins->{{8, 10}, {5, 5}}, LineSpacing->{1, 2}, FontSize->9], Cell[StyleData["SmallText", "Printout"], CellMargins->{{2, 2}, {5, 5}}, TextJustification->0.5, FontSize->7] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["Styles for Input/Output", "Section"], Cell["\<\ The cells in this section define styles used for input and output to the \ kernel. Be careful when modifying, renaming, or removing these styles, \ because the front end associates special meanings with these style names. \ Some attributes for these styles are actually set in FormatType Styles (in \ the last section of this stylesheet). \ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Input"], CellMargins->{{45, 10}, {5, 7}}, Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, DefaultFormatType->DefaultInputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, LanguageCategory->"Formula", FormatType->InputForm, ShowStringCharacters->True, NumberMarks->True, LinebreakAdjustments->{0.85, 2, 10, 0, 1}, CounterIncrements->"Input", FontWeight->"Bold"], Cell[StyleData["Input", "Presentation"], CellMargins->{{72, Inherited}, {8, 10}}, LineSpacing->{1, 0}, FontSize->16], Cell[StyleData["Input", "Condensed"], CellMargins->{{40, 10}, {2, 3}}, FontSize->11], Cell[StyleData["Input", "Printout"], CellMargins->{{39, 0}, {4, 6}}, LinebreakAdjustments->{0.85, 2, 10, 1, 1}, FontSize->9] }, Closed]], Cell[StyleData["InputOnly"], Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, LanguageCategory->"Formula", FormatType->InputForm, ShowStringCharacters->True, NumberMarks->True, LinebreakAdjustments->{0.85, 2, 10, 0, 1}, CounterIncrements->"Input", StyleMenuListing->None, FontWeight->"Bold"], Cell[CellGroupData[{ Cell[StyleData["Output"], CellMargins->{{47, 10}, {7, 5}}, CellEditDuplicate->True, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, DefaultFormatType->DefaultOutputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, LanguageCategory->"Formula", FormatType->InputForm, CounterIncrements->"Output"], Cell[StyleData["Output", "Presentation"], CellMargins->{{72, Inherited}, {10, 8}}, LineSpacing->{1, 0}, FontSize->16], Cell[StyleData["Output", "Condensed"], CellMargins->{{41, Inherited}, {3, 2}}, FontSize->11], Cell[StyleData["Output", "Printout"], CellMargins->{{39, 0}, {6, 4}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Message"], CellMargins->{{45, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"OutputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Message", StyleMenuListing->None, FontSize->11, FontColor->RGBColor[0, 0, 1]], Cell[StyleData["Message", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}, FontSize->16], Cell[StyleData["Message", "Condensed"], CellMargins->{{41, Inherited}, {Inherited, Inherited}}, FontSize->11], Cell[StyleData["Message", "Printout"], CellMargins->{{39, Inherited}, {Inherited, Inherited}}, FontSize->7, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Print"], CellMargins->{{45, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Print", StyleMenuListing->None], Cell[StyleData["Print", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}, FontSize->16], Cell[StyleData["Print", "Condensed"], CellMargins->{{41, Inherited}, {Inherited, Inherited}}, FontSize->11], Cell[StyleData["Print", "Printout"], CellMargins->{{39, Inherited}, {Inherited, Inherited}}, FontSize->8] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Graphics"], CellMargins->{{4, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"GraphicsGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, LanguageCategory->None, FormatType->InputForm, CounterIncrements->"Graphics", ImageMargins->{{43, Inherited}, {Inherited, 0}}, StyleMenuListing->None, FontFamily->"Courier", FontSize->10], Cell[StyleData["Graphics", "Presentation"], ImageMargins->{{62, Inherited}, {Inherited, 0}}], Cell[StyleData["Graphics", "Condensed"], ImageMargins->{{38, Inherited}, {Inherited, 0}}, Magnification->0.6], Cell[StyleData["Graphics", "Printout"], ImageMargins->{{30, Inherited}, {Inherited, 0}}, Magnification->0.8] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["CellLabel"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->9, FontColor->RGBColor[0, 0, 1]], Cell[StyleData["CellLabel", "Presentation"], FontSize->12], Cell[StyleData["CellLabel", "Condensed"], FontSize->9], Cell[StyleData["CellLabel", "Printout"], FontFamily->"Courier", FontSize->8, FontSlant->"Italic", FontColor->GrayLevel[0]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Inline Formatting", "Section"], Cell["\<\ These styles are for modifying individual words or letters in a cell \ exclusive of the cell tag.\ \>", "Text"], Cell[StyleData["RM"], StyleMenuListing->None, FontWeight->"Plain", FontSlant->"Plain"], Cell[StyleData["BF"], StyleMenuListing->None, FontWeight->"Bold"], Cell[StyleData["IT"], StyleMenuListing->None, FontSlant->"Italic"], Cell[StyleData["TR"], StyleMenuListing->None, FontFamily->"Times", FontWeight->"Plain", FontSlant->"Plain"], Cell[StyleData["TI"], StyleMenuListing->None, FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], Cell[StyleData["TB"], StyleMenuListing->None, FontFamily->"Times", FontWeight->"Bold", FontSlant->"Plain"], Cell[StyleData["TBI"], StyleMenuListing->None, FontFamily->"Times", FontWeight->"Bold", FontSlant->"Italic"], Cell[StyleData["MR"], StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], Cell[StyleData["MO"], StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Italic"], Cell[StyleData["MB"], StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain"], Cell[StyleData["MBO"], StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Italic"], Cell[StyleData["SR"], StyleMenuListing->None, FontFamily->"Helvetica", FontWeight->"Plain", FontSlant->"Plain"], Cell[StyleData["SO"], StyleMenuListing->None, FontFamily->"Helvetica", FontWeight->"Plain", FontSlant->"Italic"], Cell[StyleData["SB"], StyleMenuListing->None, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain"], Cell[StyleData["SBO"], StyleMenuListing->None, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Italic"], Cell[CellGroupData[{ Cell[StyleData["SO10"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->10, FontWeight->"Plain", FontSlant->"Italic"], Cell[StyleData["SO10", "Printout"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->7, FontWeight->"Plain", FontSlant->"Italic"], Cell[StyleData["SO10", "EnhancedPrintout"], StyleMenuListing->None, FontFamily->"Futura", FontSize->7, FontWeight->"Plain", FontSlant->"Italic"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Formulas and Programming", "Section"], Cell[CellGroupData[{ Cell[StyleData["InlineFormula"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Formula", ScriptLevel->1, SingleLetterItalics->True], Cell[StyleData["InlineFormula", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, LineSpacing->{1, 5}, FontSize->16], Cell[StyleData["InlineFormula", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}, FontSize->11], Cell[StyleData["InlineFormula", "Printout"], CellMargins->{{2, 0}, {6, 6}}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DisplayFormula"], CellMargins->{{42, Inherited}, {Inherited, Inherited}}, CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Formula", ScriptLevel->0, SingleLetterItalics->True, UnderoverscriptBoxOptions->{LimitsPositioning->True}], Cell[StyleData["DisplayFormula", "Presentation"], LineSpacing->{1, 5}, FontSize->16], Cell[StyleData["DisplayFormula", "Condensed"], LineSpacing->{1, 1}, FontSize->11], Cell[StyleData["DisplayFormula", "Printout"], FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Program"], CellFrame->{{0, 0}, {0.5, 0.5}}, CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, LanguageCategory->"Formula", ScriptLevel->1, FontFamily->"Courier"], Cell[StyleData["Program", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, LineSpacing->{1, 5}, FontSize->16], Cell[StyleData["Program", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}, FontSize->11], Cell[StyleData["Program", "Printout"], CellMargins->{{2, 0}, {6, 6}}, FontSize->9] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Hyperlink Styles", "Section"], Cell["\<\ The cells below define styles useful for making hypertext ButtonBoxes. The \ \"Hyperlink\" style is for links within the same Notebook, or between \ Notebooks.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Hyperlink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), Active->True, ButtonNote->ButtonData}], Cell[StyleData["Hyperlink", "Presentation"], FontSize->16], Cell[StyleData["Hyperlink", "Condensed"], FontSize->11], Cell[StyleData["Hyperlink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell["\<\ The following styles are for linking automatically to the on-line help \ system.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["MainBookLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "MainBook", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["MainBookLink", "Presentation"], FontSize->16], Cell[StyleData["MainBookLink", "Condensed"], FontSize->11], Cell[StyleData["MainBookLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["AddOnsLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "AddOns", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["AddOnsLink", "Presentation"], FontSize->16], Cell[StyleData["AddOnsLink", "Condensed"], FontSize->11], Cell[StyleData["AddOnsLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["RefGuideLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "RefGuide", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["RefGuideLink", "Presentation"], FontSize->16], Cell[StyleData["RefGuideLink", "Condensed"], FontSize->11], Cell[StyleData["RefGuideLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["GettingStartedLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "GettingStarted", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["GettingStartedLink", "Presentation"], FontSize->16], Cell[StyleData["GettingStartedLink", "Condensed"], FontSize->11], Cell[StyleData["GettingStartedLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["OtherInformationLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "OtherInformation", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["OtherInformationLink", "Presentation"], FontSize->16], Cell[StyleData["OtherInformationLink", "Condensed"], FontSize->11], Cell[StyleData["OtherInformationLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Headers and Footers", "Section"], Cell[StyleData["Header"], CellMargins->{{0, 0}, {4, 1}}, DefaultNewInlineCellStyle->"None", LanguageCategory->"NaturalLanguage", StyleMenuListing->None, FontSize->10, FontSlant->"Italic"], Cell[StyleData["Footer"], CellMargins->{{0, 0}, {0, 4}}, DefaultNewInlineCellStyle->"None", LanguageCategory->"NaturalLanguage", StyleMenuListing->None, FontSize->9, FontSlant->"Italic"], Cell[StyleData["PageNumber"], CellMargins->{{0, 0}, {4, 1}}, StyleMenuListing->None, FontFamily->"Times", FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell["Palette Styles", "Section"], Cell["\<\ The cells below define styles that define standard ButtonFunctions, for use \ in palette buttons.\ \>", "Text"], Cell[StyleData["Paste"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, After]}]&)}], Cell[StyleData["Evaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["EvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionMove[ FrontEnd`InputNotebook[ ], All, Cell, 1], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}] }, Closed]], Cell[CellGroupData[{ Cell["Placeholder Styles", "Section"], Cell["\<\ The cells below define styles useful for making placeholder objects in \ palette templates.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Placeholder"], Placeholder->True, StyleMenuListing->None, FontSlant->"Italic", FontColor->RGBColor[0.890623, 0.864698, 0.384756], TagBoxOptions->{Editable->False, Selectable->False, StripWrapperBoxes->False}], Cell[StyleData["Placeholder", "Presentation"]], Cell[StyleData["Placeholder", "Condensed"]], Cell[StyleData["Placeholder", "Printout"]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["PrimaryPlaceholder"], StyleMenuListing->None, DrawHighlighted->True, FontSlant->"Italic", Background->RGBColor[0.912505, 0.891798, 0.507774], TagBoxOptions->{Editable->False, Selectable->False, StripWrapperBoxes->False}], Cell[StyleData["PrimaryPlaceholder", "Presentation"]], Cell[StyleData["PrimaryPlaceholder", "Condensed"]], Cell[StyleData["PrimaryPlaceholder", "Printout"]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["FormatType Styles", "Section"], Cell["\<\ The cells below define styles that are mixed in with the styles of most \ cells. If a cell's FormatType matches the name of one of the styles defined \ below, then that style is applied between the cell's style and its own \ options. This is particularly true of Input and Output.\ \>", "Text"], Cell[StyleData["CellExpression"], PageWidth->Infinity, CellMargins->{{6, Inherited}, {Inherited, Inherited}}, ShowCellLabel->False, ShowSpecialCharacters->False, AllowInlineCells->False, Hyphenation->False, AutoItalicWords->{}, StyleMenuListing->None, FontFamily->"Courier", FontSize->12, Background->GrayLevel[1]], Cell[StyleData["InputForm"], InputAutoReplacements->{}, AllowInlineCells->False, Hyphenation->False, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["OutputForm"], PageWidth->Infinity, TextAlignment->Left, LineSpacing->{0.6, 1}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["StandardForm"], InputAutoReplacements->{ "->"->"\[Rule]", ":>"->"\[RuleDelayed]", "<="->"\[LessEqual]", ">="->"\[GreaterEqual]", "!="->"\[NotEqual]", "=="->"\[Equal]", Inherited}, LineSpacing->{1.25, 0}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["TraditionalForm"], InputAutoReplacements->{ "->"->"\[Rule]", ":>"->"\[RuleDelayed]", "<="->"\[LessEqual]", ">="->"\[GreaterEqual]", "!="->"\[NotEqual]", "=="->"\[Equal]", Inherited}, LineSpacing->{1.25, 0}, SingleLetterItalics->True, TraditionalFunctionNotation->True, DelimiterMatching->None, StyleMenuListing->None], Cell["\<\ The style defined below is mixed in to any cell that is in an inline cell \ within another.\ \>", "Text"], Cell[StyleData["InlineCell"], TextAlignment->Left, ScriptLevel->1, StyleMenuListing->None], Cell[StyleData["InlineCellEditing"], StyleMenuListing->None, Background->RGBColor[1, 0.749996, 0.8]] }, Closed]], Cell[CellGroupData[{ Cell["Automatic Styles", "Section"], Cell["\<\ The cells below define styles that are used to affect the display of certain \ types of objects in typeset expressions. For example, \"UnmatchedBracket\" \ style defines how unmatched bracket, curly bracket, and parenthesis \ characters are displayed (typically by coloring them to make them stand out).\ \ \>", "Text"], Cell[StyleData["UnmatchedBracket"], StyleMenuListing->None, FontColor->RGBColor[0.760006, 0.330007, 0.8]] }, Closed]] }, Open ]] }] ] (*********************************************************************** Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. 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