(* 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[ 3600, 130] NotebookOptionsPosition[ 3165, 110] NotebookOutlinePosition[ 3508, 125] CellTagsIndexPosition[ 3465, 122] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"A", " ", "=", " ", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"vdown", " ", RowBox[{"(", " ", RowBox[{"1", " ", "-", " ", "m"}], " ", ")"}], " ", "d"}], " ", "+", " ", RowBox[{"vup", " ", RowBox[{"(", " ", RowBox[{"1", " ", "-", " ", "d"}], " ", ")"}], " ", RowBox[{"(", " ", RowBox[{"1", " ", "+", " ", "m"}], " ", ")"}]}]}], ")"}], " "}], RowBox[{"1", " ", "-", " ", RowBox[{"m", " ", RowBox[{"(", " ", RowBox[{"1", " ", "-", " ", RowBox[{"2", " ", "d"}]}], " ", ")"}]}]}]]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"B", " ", "=", " ", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"vdown", " ", RowBox[{"(", " ", RowBox[{"1", " ", "+", " ", "m"}], " ", ")"}], " ", "d"}], " ", "+", " ", RowBox[{"vup", " ", RowBox[{"(", " ", RowBox[{"1", " ", "-", " ", "d"}], " ", ")"}], " ", RowBox[{"(", " ", RowBox[{"1", " ", "-", " ", "m"}], " ", ")"}]}]}], ")"}], " "}], RowBox[{"1", " ", "+", " ", RowBox[{"m", " ", RowBox[{"(", " ", RowBox[{"1", " ", "-", " ", RowBox[{"2", " ", "d"}]}], " ", ")"}]}]}]]}], ";"}], "\[IndentingNewLine]", RowBox[{"spread", "=", RowBox[{"Simplify", "[", RowBox[{"A", "-", "B"}], "]"}]}]}], "Input", CellChangeTimes->{{3.543061160069866*^9, 3.5430612195548744`*^9}, { 3.543061613574679*^9, 3.5430616147465687`*^9}}], Cell[BoxData[ FractionBox[ RowBox[{"4", " ", "m", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["d", "2"], " ", RowBox[{"(", RowBox[{"vdown", "-", "vup"}], ")"}]}], "-", "vup", "+", RowBox[{"2", " ", "d", " ", "vup"}]}], ")"}]}], RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", RowBox[{"2", " ", "d"}]}], ")"}], "2"], " ", SuperscriptBox["m", "2"]}]}]]], "Output", CellChangeTimes->{3.5430612202580085`*^9, 3.5430612917118883`*^9, 3.5430616152309504`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"spread", "/.", RowBox[{"{", RowBox[{"d", "\[Rule]", FractionBox["1", "2"]}], "}"}]}]], "Input", CellChangeTimes->{{3.543061615996585*^9, 3.543061627746724*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"-", "m"}], " ", RowBox[{"(", RowBox[{"vdown", "-", "vup"}], ")"}]}]], "Output", CellChangeTimes->{3.543061628981094*^9}] }, Open ]] }, WindowSize->{616, 750}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, FrontEndVersion->"7.0 for Microsoft Windows (32-bit) (February 18, 2009)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[567, 22, 1590, 47, 108, "Input"], Cell[2160, 71, 589, 19, 53, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[2786, 95, 197, 5, 47, "Input"], Cell[2986, 102, 163, 5, 30, "Output"] }, Open ]] } ] *) (* End of internal cache information *)