(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 7.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 616660, 10335] NotebookOptionsPosition[ 614828, 10280] NotebookOutlinePosition[ 615884, 10310] CellTagsIndexPosition[ 615841, 10307] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Initialization", "Section", CellChangeTimes->{{3.523641507003084*^9, 3.523641512076024*^9}, 3.523642192173356*^9, {3.523644576290742*^9, 3.523644619859024*^9}, { 3.5236446528454323`*^9, 3.523644701763885*^9}, {3.524962393830915*^9, 3.524962397451693*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"SetOptions", "[", RowBox[{"Plot", ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"Blue", ",", RowBox[{"AbsoluteThickness", "[", "2", "]"}], ",", " ", "Dashed"}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", "500"}], ",", RowBox[{"AxesStyle", "\[Rule]", RowBox[{"Directive", "[", RowBox[{ RowBox[{"FontFamily", "\[Rule]", "\"\\""}], ",", RowBox[{"FontSize", "\[Rule]", "18"}], ",", "Black", ",", RowBox[{"AbsoluteThickness", "[", "0.5", "]"}], ",", RowBox[{"Arrowheads", "[", "0.04", "]"}]}], "]"}]}]}], "]"}], ";"}]], "Input", CellChangeTimes->{{3.523641600820446*^9, 3.5236416366263447`*^9}, { 3.523641983662058*^9, 3.523641990235628*^9}, {3.523642371794956*^9, 3.523642423427026*^9}, {3.523642457933744*^9, 3.523642477692999*^9}, { 3.523643528261017*^9, 3.523643537402582*^9}, {3.523643789219001*^9, 3.5236437902211*^9}, {3.523643880766148*^9, 3.523643888421876*^9}, { 3.5236439378333063`*^9, 3.523643952543745*^9}, {3.523644295646544*^9, 3.5236443193414907`*^9}, {3.523647501855562*^9, 3.523647532459059*^9}, { 3.5249651647864447`*^9, 3.524965218185865*^9}, {3.524965265068446*^9, 3.524965308795487*^9}, {3.5249660310374813`*^9, 3.5249660484914627`*^9}, { 3.524968448550538*^9, 3.524968484654293*^9}}] }, Open ]], Cell["Work", "Section", CellChangeTimes->{{3.5236475663203773`*^9, 3.523647567328497*^9}}], Cell[CellGroupData[{ Cell["Y_lm", "Title", CellChangeTimes->{{3.523646269289253*^9, 3.523646276119632*^9}, { 3.524963254993203*^9, 3.52496326349609*^9}, {3.524967434254039*^9, 3.524967442330435*^9}, {3.537136177295986*^9, 3.537136177572003*^9}, { 3.542544743620615*^9, 3.542544768416006*^9}, 3.542590902539217*^9, 3.5736690832743397`*^9}], Cell["Basics", "Subtitle", CellChangeTimes->{{3.537136200381118*^9, 3.537136201524106*^9}}], Cell["\<\ This worksheet plots the complex (Y_lm; with l the angular momentum qn and m \ the magnetic or projection qn) spherical harmonics, and shows that the Y_lm \ functions are orthogonal by projecting one onto another.\ \>", "Text", CellChangeTimes->{{3.524963542397662*^9, 3.524963623700782*^9}, { 3.5249664582613697`*^9, 3.524966586228037*^9}, {3.524966628428534*^9, 3.5249666319649076`*^9}, {3.5249675801847363`*^9, 3.5249675855048103`*^9}, {3.524967723578019*^9, 3.524967736138319*^9}, { 3.524967836569661*^9, 3.524967849034729*^9}, 3.5249702164062757`*^9, { 3.5425831112937593`*^9, 3.5425831866446342`*^9}, {3.542588522784725*^9, 3.542588561261826*^9}, {3.542588683274559*^9, 3.542588732850535*^9}, { 3.573669077237693*^9, 3.573669113147025*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"l1", "=", "1"}], ";", RowBox[{"m1", "=", "0"}], ";", RowBox[{"l2", "=", "1"}], ";", RowBox[{"m2", "=", "1"}], ";", RowBox[{"Integrate", "[", RowBox[{ RowBox[{ RowBox[{"SphericalHarmonicY", "[", RowBox[{"l1", ",", "m1", ",", "\[Theta]", ",", "\[Phi]"}], "]"}], "*", RowBox[{"Conjugate", "[", RowBox[{"SphericalHarmonicY", "[", RowBox[{"l2", ",", "m2", ",", "\[Theta]", ",", "\[Phi]"}], "]"}], "]"}], "*", RowBox[{"Sin", "[", "\[Theta]", "]"}]}], ",", RowBox[{"{", RowBox[{"\[Theta]", ",", "0", ",", "Pi"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Phi]", ",", "0", ",", RowBox[{"2", "*", "Pi"}]}], "}"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.542588596177085*^9, 3.54258866729219*^9}}], Cell[BoxData["0"], "Output", CellChangeTimes->{{3.5425886581644*^9, 3.54258866805161*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["Plots", "Subtitle", CellChangeTimes->{{3.537136249348321*^9, 3.5371362536204033`*^9}}], Cell[TextData[{ "Plot any real spherical harmonic with the SphericalPlot3D function. 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