(* ::Package:: *)

(************************************************************************)
(* This file was generated automatically by the Mathematica front end.  *)
(* It contains Initialization cells from a Notebook file, which         *)
(* typically will have the same name as this file except ending in      *)
(* ".nb" instead of ".m".                                               *)
(*                                                                      *)
(* This file is intended to be loaded into the Mathematica kernel using *)
(* the package loading commands Get or Needs.  Doing so is equivalent   *)
(* to using the Evaluate Initialization Cells menu command in the front *)
(* end.                                                                 *)
(*                                                                      *)
(* DO NOT EDIT THIS FILE.  This entire file is regenerated              *)
(* automatically each time the parent Notebook file is saved in the     *)
(* Mathematica front end.  Any changes you make to this file will be    *)
(* overwritten.                                                         *)
(************************************************************************)



(* ::Input::Initialization:: *)
ME[x_] := MatrixExp[x]; MF[x_] := MatrixForm[x];


(* ::Input::Initialization:: *)
q=E^(\[HBar] \[Gamma] \[Epsilon]); \[Rho]I=({
 {1, 0},
 {0, 1}
}); \[Rho]y=\!\(\*
TagBox[
RowBox[{"(", "", GridBox[{
{"0", "0"},
{
RowBox[{"-", "1"}], "0"}
},
GridBoxAlignment->{"Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}, "Items" -> {}, "ItemsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {Offset[0.27999999999999997`], {Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {Offset[0.2], {Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}, "Items" -> {}, "ItemsIndexed" -> {}}], "", ")"}],
Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]\); \[Rho]a=\!\(\*
TagBox[
RowBox[{"(", "", GridBox[{
{"0", "0"},
{"0", 
RowBox[{"-", "\[Gamma]"}]}
},
GridBoxAlignment->{"Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}, "Items" -> {}, "ItemsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {Offset[0.27999999999999997`], {Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {Offset[0.2], {Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}, "Items" -> {}, "ItemsIndexed" -> {}}], "", ")"}],
Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]\);\[Rho]x=\!\(\*
TagBox[
RowBox[{"(", "", GridBox[{
{"0", 
FractionBox[
RowBox[{
RowBox[{"-", "1"}], "+", 
SuperscriptBox["E", 
RowBox[{
RowBox[{"-", "\[Gamma]"}], " ", "\[Epsilon]", " ", "\[HBar]"}]]}], "\[HBar]"]},
{"0", "0"}
},
GridBoxAlignment->{"Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}, "Items" -> {}, "ItemsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {Offset[0.27999999999999997`], {Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {Offset[0.2], {Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}, "Items" -> {}, "ItemsIndexed" -> {}}], "", ")"}],
Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]\); \[Rho]b=\!\(\*
TagBox[
RowBox[{"(", "", GridBox[{
{"\[Epsilon]", "0"},
{"0", "0"}
},
GridBoxAlignment->{"Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}, "Items" -> {}, "ItemsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {Offset[0.27999999999999997`], {Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {Offset[0.2], {Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}, "Items" -> {}, "ItemsIndexed" -> {}}], "", ")"}],
Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]\);
\[Rho]t=Simplify[\[Epsilon] \[Rho]a-\[Gamma] \[Rho]b]; \[Rho]A=ME[-\[HBar] \[Epsilon] \[Rho]a];  \[Rho]B=ME[-\[HBar] \[Gamma] \[Rho]b];  \[Rho]T=ME[\[HBar] \[Rho]t];
(#->MF@Simplify@ToExpression@#)& /@ {"{{q}}", "\[Rho]y","\[Rho]a","\[Rho]x","\[Rho]b", "\[Rho]t", "\[Rho]A", "\[Rho]B", "\[Rho]T", "\[Rho]I"}


(* ::Input::Initialization:: *)
{\[Rho]a.\[Rho]x-\[Rho]x.\[Rho]a==\[Gamma] \[Rho]x, \[Rho]x.\[Rho]A==q \[Rho]A.\[Rho]x, \[Rho]a.\[Rho]y-\[Rho]y.\[Rho]a==-\[Gamma] \[Rho]y, \[Rho]b.\[Rho]y-\[Rho]y.\[Rho]b==-\[Epsilon] \[Rho]y, \[Rho]x.\[Rho]y-q \[Rho]y.\[Rho]x==(\[Rho]I-\[Rho]T.\[Rho]A.\[Rho]A)/\[HBar]} // Simplify



