(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 11.1' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 9709, 292] NotebookOptionsPosition[ 7866, 238] NotebookOutlinePosition[ 8210, 253] CellTagsIndexPosition[ 8167, 250] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Representando as fun\[CCedilla]\[OTilde]es de onda angulares", "Title", CellChangeTimes->{{3.719163570931831*^9, 3.7191635826332784`*^9}},ExpressionUUID->"8c0d1364-e48a-4ffa-86cb-\ 4cb1f6a16c4f"], Cell[CellGroupData[{ Cell["F\[OAcute]rmulas anal\[IAcute]ticas", "Section", CellChangeTimes->{{3.7191675867489843`*^9, 3.71916759087607*^9}},ExpressionUUID->"05876292-811e-4bdd-968f-\ 579e0ad04f47"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"SphericalHarmonicY", "[", RowBox[{"3", ",", "2", ",", "\[Theta]", ",", "\[Phi]"}], "]"}]], "Input", CellChangeTimes->{{3.719163591072381*^9, 3.719163600514268*^9}, { 3.7191636864695063`*^9, 3.7191636950778966`*^9}},ExpressionUUID->"3425dc6b-4f7f-47cd-991d-\ 7374bfb316ab"], Cell[BoxData[ RowBox[{ FractionBox["1", "4"], " ", SuperscriptBox["\[ExponentialE]", RowBox[{"2", " ", "\[ImaginaryI]", " ", "\[Phi]"}]], " ", SqrtBox[ FractionBox["105", RowBox[{"2", " ", "\[Pi]"}]]], " ", RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", SuperscriptBox[ RowBox[{"Sin", "[", "\[Theta]", "]"}], "2"]}]], "Output", CellChangeTimes->{3.719163696898553*^9, 3.719167859534482*^9},ExpressionUUID->"06c2393d-5b93-4d7f-aad1-\ 215e328e71a6"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{" ", RowBox[{ RowBox[{"SphericalHarmonicY", "[", RowBox[{"3", ",", "2", ",", "\[Theta]", ",", "\[Phi]"}], "]"}], " ", "//", "ExpToTrig"}]}]], "Input", CellChangeTimes->{{3.7191679448510904`*^9, 3.719168018855941*^9}},ExpressionUUID->"27b22e28-a4fc-4e62-a61c-\ 22ecc0d29329"], Cell[BoxData[ RowBox[{ FractionBox["1", "4"], " ", SqrtBox[ FractionBox["105", RowBox[{"2", " ", "\[Pi]"}]]], " ", RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", SuperscriptBox[ RowBox[{"Sin", "[", "\[Theta]", "]"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", RowBox[{"2", " ", "\[Phi]"}], "]"}], "+", RowBox[{"\[ImaginaryI]", " ", RowBox[{"Sin", "[", RowBox[{"2", " ", "\[Phi]"}], "]"}]}]}], ")"}]}]], "Output", CellChangeTimes->{{3.71916795217148*^9, 3.719168019820962*^9}},ExpressionUUID->"d0666eb9-f276-43f9-8754-\ b37e49e87eee"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"LegendreP", "[", RowBox[{"3", ",", "3", ",", "x"}], "]"}]], "Input", CellChangeTimes->{{3.719167378518381*^9, 3.719167383299034*^9}},ExpressionUUID->"00914568-9d6e-4ba8-b9fa-\ 2c1b30d4988b"], Cell[BoxData[ RowBox[{ RowBox[{"-", "15"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", SuperscriptBox["x", "2"]}], ")"}], RowBox[{"3", "/", "2"}]]}]], "Output", CellChangeTimes->{3.7191673838538313`*^9, 3.719167859717326*^9},ExpressionUUID->"b157ac1d-0803-4815-846e-\ c507a8e4408f"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Gr\[AAcute]ficos 3D", "Section", CellChangeTimes->{{3.719167596939734*^9, 3.719167599731931*^9}},ExpressionUUID->"67fd0eb8-97c4-4b2c-94b4-\ 2b64f2e54656"], Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"SphericalPlot3D", "[", RowBox[{ RowBox[{"Evaluate", "[", RowBox[{ RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", "m", ",", "\[Theta]", ",", "\[Phi]"}], "]"}], " ", RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", RowBox[{"-", "m"}], ",", "\[Theta]", ",", "\[Phi]"}], "]"}]}], "]"}], ",", RowBox[{"{", RowBox[{"\[Theta]", ",", "0", ",", "Pi"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Phi]", ",", "0", ",", RowBox[{"2", "Pi"}]}], "}"}], ",", RowBox[{"PerformanceGoal", "\[Rule]", "\"\\""}], ",", RowBox[{"AspectRatio", "\[Rule]", "Automatic"}]}], "]"}], ",", RowBox[{"{", RowBox[{"l", ",", "0", ",", "7", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"m", ",", "0", ",", "l", ",", "1"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.7191637033320723`*^9, 3.7191637079826927`*^9}, { 3.7191638312563314`*^9, 3.719163933325055*^9}, {3.719163963339925*^9, 3.7191639714938006`*^9}, {3.719164037767338*^9, 3.7191641999259844`*^9}, { 3.719164301538289*^9, 3.719164306969014*^9}, {3.719167012153313*^9, 3.7191670188030205`*^9}, {3.719167060588503*^9, 3.7191670641139135`*^9}},ExpressionUUID->"b4141710-e21d-4ffe-8507-\ 64d034992071"], Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"SphericalPlot3D", "[", RowBox[{ RowBox[{"Evaluate", "[", RowBox[{ RowBox[{"LegendreP", "[", RowBox[{"l", ",", "m", ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}], " ", "^", "2"}], "]"}], ",", RowBox[{"{", RowBox[{"\[Theta]", ",", "0", ",", "Pi"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Phi]", ",", "0", ",", RowBox[{"2", "Pi"}]}], "}"}], ",", RowBox[{"PerformanceGoal", "\[Rule]", "\"\\""}], ",", RowBox[{"AspectRatio", "\[Rule]", "Automatic"}]}], "]"}], ",", RowBox[{"{", RowBox[{"l", ",", "0", ",", "7", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"m", ",", "0", ",", "l", ",", "1"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.719167468912098*^9, 3.719167541754669*^9}},ExpressionUUID->"a0e8d787-3c2b-47e5-84ce-\ a58155e4a953"], Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"SphericalPlot3D", "[", RowBox[{ RowBox[{"Evaluate", "[", RowBox[{"Re", "[", RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", "m", ",", "\[Theta]", ",", "\[Phi]"}], "]"}], " ", "]"}], "]"}], ",", RowBox[{"{", RowBox[{"\[Theta]", ",", "0", ",", "Pi"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Phi]", ",", "0", ",", RowBox[{"2", "Pi"}]}], "}"}], ",", RowBox[{"PerformanceGoal", "\[Rule]", "\"\\""}], ",", RowBox[{"AspectRatio", "\[Rule]", "Automatic"}]}], "]"}], ",", RowBox[{"{", RowBox[{"l", ",", "0", ",", "7", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"m", ",", "0", ",", "l", ",", "1"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.719167905683113*^9, 3.719167914767215*^9}},ExpressionUUID->"15766f74-0a30-4c25-b02d-\ 816cdfbbae8f"] }, Open ]], Cell[CellGroupData[{ Cell["Gr\[AAcute]fico da parte \[Theta] do harm\[OHat]nico esf\[EAcute]rico", \ "Section", CellChangeTimes->{{3.719167624839609*^9, 3.71916765871189*^9}},ExpressionUUID->"fdf291e7-7fbc-49f7-a4f9-\ 7617e2937eee"], Cell[BoxData[ RowBox[{"Manipulate", "[", " ", RowBox[{ RowBox[{"Plot", "[", RowBox[{ RowBox[{"LegendreP", "[", RowBox[{"l", ",", "m", ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}], ",", RowBox[{"{", RowBox[{"\[Theta]", ",", "0", ",", "Pi"}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"l", ",", "0", ",", "7", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"m", ",", "0", ",", "l", ",", "1"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.719164342652461*^9, 3.7191643753747597`*^9}, { 3.719167120501026*^9, 3.7191671450983152`*^9}, {3.7191671916348157`*^9, 3.719167200824576*^9}, {3.719167359802356*^9, 3.7191673619082246`*^9}, { 3.719167392560518*^9, 3.719167416848174*^9}},ExpressionUUID->"7f6b0824-6278-4ce5-9f9c-\ 9d53345b3162"] }, Open ]] }, Open ]] }, WindowSize->{996, 833}, WindowMargins->{{Automatic, 335}, {64, Automatic}}, FrontEndVersion->"11.1 for Microsoft Windows (64-bit) (April 18, 2017)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[580, 22, 205, 3, 101, "Title", "ExpressionUUID" -> \ "8c0d1364-e48a-4ffa-86cb-4cb1f6a16c4f"], Cell[CellGroupData[{ Cell[810, 29, 181, 3, 70, "Section", "ExpressionUUID" -> \ "05876292-811e-4bdd-968f-579e0ad04f47"], Cell[CellGroupData[{ Cell[1016, 36, 305, 6, 30, "Input", "ExpressionUUID" -> \ "3425dc6b-4f7f-47cd-991d-7374bfb316ab"], Cell[1324, 44, 478, 13, 71, "Output", "ExpressionUUID" -> \ "06c2393d-5b93-4d7f-aad1-215e328e71a6"] }, Open ]], Cell[CellGroupData[{ Cell[1839, 62, 316, 8, 30, "Input", "ExpressionUUID" -> \ "27b22e28-a4fc-4e62-a61c-22ecc0d29329"], Cell[2158, 72, 602, 18, 71, "Output", "ExpressionUUID" -> \ "d0666eb9-f276-43f9-8754-b37e49e87eee"] }, Open ]], Cell[CellGroupData[{ Cell[2797, 95, 221, 5, 30, "Input", "ExpressionUUID" -> \ "00914568-9d6e-4ba8-b9fa-2c1b30d4988b"], Cell[3021, 102, 319, 10, 34, "Output", "ExpressionUUID" -> \ "b157ac1d-0803-4815-846e-c507a8e4408f"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[3389, 118, 164, 3, 70, "Section", "ExpressionUUID" -> \ "67fd0eb8-97c4-4b2c-94b4-2b64f2e54656"], Cell[3556, 123, 1351, 30, 50, "Input", "ExpressionUUID" -> \ "b4141710-e21d-4ffe-8507-64d034992071"], Cell[4910, 155, 932, 24, 50, "Input", "ExpressionUUID" -> \ "a0e8d787-3c2b-47e5-84ce-a58155e4a953"], Cell[5845, 181, 926, 23, 50, "Input", "ExpressionUUID" -> \ "15766f74-0a30-4c25-b02d-816cdfbbae8f"] }, Open ]], Cell[CellGroupData[{ Cell[6808, 209, 215, 4, 70, "Section", "ExpressionUUID" -> \ "fdf291e7-7fbc-49f7-a4f9-7617e2937eee"], Cell[7026, 215, 812, 19, 30, "Input", "ExpressionUUID" -> \ "7f6b0824-6278-4ce5-9f9c-9d53345b3162"] }, Open ]] }, Open ]] } ] *)