(* ::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=MatrixExp; MF=MatrixForm;


(* ::Input::Initialization:: *)
\[HBar]=(\[Sigma]-\[Rho])/(\[Gamma] \[Beta]); q=E^(\[HBar] \[Gamma] \[Beta]);
y=({
 {0, 0},
 {-E^\[Rho], 0}
}); a=\[Gamma]/(\[Rho]-\[Sigma]) ({
 {\[Rho], 0},
 {0, \[Sigma]}
});x=(E^-\[Sigma]-E^-\[Rho])/\[HBar] ({
 {0, 1},
 {0, 0}
}); b=\[Beta]/(\[Sigma]-\[Rho]) ({
 {\[Sigma], 0},
 {0, \[Rho]}
});
MF /@ {A=ME[-\[HBar] \[Beta] a], B=ME[-\[HBar] \[Gamma] b], t=Simplify[\[Beta] a-\[Gamma] b] , T=ME[\[HBar] t]}


(* ::Input::Initialization:: *)
{a.x-x.a==\[Gamma] x, x.A==q A.x, a.y-y.a==-\[Gamma] y, b.y-y.b==-\[Beta] y, x.y-q y.x==(({
 {1, 0},
 {0, 1}
})-T.A.A)/\[HBar]} // Simplify


(* ::Input::Initialization:: *)
Clear[\[HBar]]; \[Rho]=0; \[Sigma]=\[HBar] \[Beta] \[Gamma];
t=Simplify[\[Beta] a-\[Gamma] b]; A=ME[-\[Beta] a/\[Gamma]];  B=ME[-b];  T=ME[t/\[Gamma]];
(#->MF@Simplify@ToExpression@#)& /@ {"{{q}}", "y","a","x","b", "t", "A", "B", "T"}



