(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 10.3' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 55336, 1220] NotebookOptionsPosition[ 53437, 1148] NotebookOutlinePosition[ 53822, 1165] CellTagsIndexPosition[ 53779, 1162] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Fermiones no relativistas en 3D", "Title", CellChangeTimes->{{3.6561405047599363`*^9, 3.656140513140992*^9}}], Cell[CellGroupData[{ Cell["\<\ Densidad de particulas en funcion de z y T. Se usa densidad de estados \ Sqrt[eps]\ \>", "Subsubsection", CellChangeTimes->{{3.656140527493294*^9, 3.656140540947897*^9}, { 3.656140710766788*^9, 3.656140722549601*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Integrate", "[", RowBox[{ RowBox[{ RowBox[{"Sqrt", "[", "x", "]"}], "/", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"z", "^", RowBox[{"(", RowBox[{"-", "1"}], ")"}]}], " ", RowBox[{"Exp", "[", "x", "]"}]}], "+", "1"}], ")"}]}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "Infinity"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{3.6561396762313137`*^9}], Cell[BoxData[ RowBox[{ RowBox[{"-", FractionBox["1", "2"]}], " ", SqrtBox["\[Pi]"], " ", RowBox[{"PolyLog", "[", RowBox[{ FractionBox["3", "2"], ",", RowBox[{"-", "z"}]}], "]"}]}]], "Output", CellChangeTimes->{3.656157234189198*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"n", "[", RowBox[{"z_", ",", "T_"}], "]"}], "=", RowBox[{ RowBox[{"T", "^", RowBox[{"(", RowBox[{"3", "/", "2"}], ")"}]}], " ", RowBox[{"Integrate", "[", RowBox[{ RowBox[{ RowBox[{"Sqrt", "[", "x", "]"}], "/", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"z", "^", RowBox[{"(", RowBox[{"-", "1"}], ")"}]}], " ", RowBox[{"Exp", "[", "x", "]"}]}], "+", "1"}], ")"}]}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "Infinity"}], "}"}]}], "]"}]}]}]], "Input", CellChangeTimes->{ 3.656139233190963*^9, {3.6561396791274223`*^9, 3.65613968646124*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"-", FractionBox["1", "2"]}], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["T", RowBox[{"3", "/", "2"}]], " ", RowBox[{"PolyLog", "[", RowBox[{ FractionBox["3", "2"], ",", RowBox[{"-", "z"}]}], "]"}]}]], "Output", CellChangeTimes->{3.656157247326174*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Se invierte la relacion. z en funcion de n y T. 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