diff --git a/doc/api-doc/Perturbation.nb b/doc/api-doc/Perturbation.nb index f08f024..2c118d7 100644 --- a/doc/api-doc/Perturbation.nb +++ b/doc/api-doc/Perturbation.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 145301, 3773] -NotebookOptionsPosition[ 135860, 3469] -NotebookOutlinePosition[ 138188, 3534] -CellTagsIndexPosition[ 137586, 3518] +NotebookDataLength[ 149988, 3900] +NotebookOptionsPosition[ 139857, 3573] +NotebookOutlinePosition[ 142330, 3642] +CellTagsIndexPosition[ 141688, 3625] WindowFrame->Normal*) (* Beginning of Notebook Content *) @@ -32,6 +32,8 @@ Cell[CellGroupData[{ Cell["Preamble", "Subsection", CellChangeTimes->{{3.636379689161282*^9, 3.6363796904310207`*^9}}], +Cell[CellGroupData[{ + Cell[BoxData[ RowBox[{"Needs", "[", "\"\\"", "]"}]], "Input", CellChangeTimes->{{3.633351696261045*^9, 3.633351701530016*^9}, { @@ -40,6 +42,20 @@ Cell[BoxData[ 3.633781401233733*^9, 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Cell[CellGroupData[{ -Cell[73626, 2321, 1807, 42, 148, "Input"], -Cell[75436, 2365, 59987, 1085, 266, "Output"] +Cell[74373, 2321, 1807, 42, 187, "Input"], +Cell[76183, 2365, 59932, 1080, 267, "Output"] }, Open ]] }, Closed]] }, Open ]], Cell[CellGroupData[{ -Cell[135484, 3457, 97, 1, 44, "Subsection"], -Cell[135584, 3460, 236, 4, 31, "Text"] +Cell[136176, 3452, 97, 1, 44, "Subsection"], +Cell[136276, 3455, 236, 4, 33, "Text"] }, Closed]] +}, Open ]], +Cell[CellGroupData[{ +Cell[136561, 3465, 97, 1, 65, "Section"], +Cell[CellGroupData[{ +Cell[136683, 3470, 100, 1, 45, "Subsection"], +Cell[136786, 3473, 1688, 50, 50, "Text", + CellTags->"BCHExpansion::usage"], +Cell[CellGroupData[{ +Cell[138499, 3527, 100, 1, 35, "Subsubsection"], +Cell[138602, 3530, 338, 8, 55, "Input"], +Cell[CellGroupData[{ +Cell[138965, 3542, 204, 4, 32, "Input"], +Cell[139172, 3548, 621, 18, 34, "Output"] +}, Open ]] +}, Closed]] +}, Open ]] }, Open ]] }, Open ]] } ] *) -(* End of internal cache information *) diff --git a/src/Perturbation.m b/src/Perturbation.m index 8c012cc..e00e576 100644 --- a/src/Perturbation.m +++ b/src/Perturbation.m @@ -40,7 +40,7 @@ (*Usage Declarations*) -(* ::Subsection:: *) +(* ::Subsection::Closed:: *) (*Magnus Expansion*) @@ -75,7 +75,7 @@ AssignUsage[SecondOrderEigenvalue,$PerturbationsUsages]; -(* ::Subsection:: *) +(* ::Subsection::Closed:: *) (*Zassenhaus Expansion*) @@ -88,14 +88,24 @@ AssignUsage[ClearZassenhausCache,$PerturbationsUsages]; -(* ::Section:: *) +(* ::Subsection::Closed:: *) +(*BCH Expansion *) + + +Unprotect[BCHExpansion] + + +AssignUsage[BCHExpansion,$PerturbationsUsages]; + + +(* ::Section::Closed:: *) (*Implementation*) Begin["`Private`"]; -(* ::Subsection:: *) +(* ::Subsection::Closed:: *) (*Magnus Expansion*) @@ -196,7 +206,7 @@ MagnusConvergenceTest[{A_,tf_},opts:OptionsPattern[]]:=MagnusConvergenceTest[{A,0,tf},opts] -(* ::Subsection:: *) +(* ::Subsection::Closed:: *) (*Average Hamiltonian*) @@ -363,7 +373,7 @@ ] -(* ::Subsection:: *) +(* ::Subsection::Closed:: *) (*Zassenhaus Expansion*) @@ -428,7 +438,7 @@ (* ::Text:: *) -(*Cached function*) +(*Cached function *) Clear[ZassenhausExpansionCached]; @@ -449,6 +459,21 @@ ZassenhausExpansion[\[Lambda]_:1,X_,Y_,n_]:=ZassenhausExpansionCached[\[Lambda],X,Y,n] +(* ::Subsection::Closed:: *) +(*BCH Expansion*) + + +(* ::Text:: *) +(*Computes Ad_(e^X)Y using a nested list to order n. *) + + +(* ::Subsubsection:: *) +(*BCH Expansion*) + + +BCHExpansion[\[Lambda]_,X_,Y_,n_]:= First[Collect[Total[NestList[Com[#,X]&,Y,n]*(Factorial/@Range[n+1])*(Power[\[Lambda],#]&/@Range[0,n])],\[Lambda],#&,Defer[+##]&]]; + + (* ::Subsection::Closed:: *) (*End Private*) @@ -456,7 +481,7 @@ End[]; -(* ::Section:: *) +(* ::Section::Closed:: *) (*End Package*) @@ -468,6 +493,7 @@ Protect[AverageHamiltonianTerm,AverageHamiltonian]; Protect[FirstOrderEigenvector,SecondOrderEigenvalue]; Protect[ZassenhausSeries,ZassenhausTerm,ZassenhausExpansion,ClearZassenhausCache]; +Protect[BCHExpansion]; EndPackage[];