(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.1' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 93337, 2617]*) (*NotebookOutlinePosition[ 93987, 2640]*) (* CellTagsIndexPosition[ 93943, 2636]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Coulomb Wave Function", "Subtitle"], Cell[CellGroupData[{ Cell[BoxData[ \(Coul[n_, l_, z_, r_]\ = \ \ \ Sqrt[ z\ \(\((n + l)\)!\)/\(\((n - l - 1)\)!\)]/\((n\ \(\((2 l + 1)\)!\))\)\ \((2\ z\ r/n)\)^\((l + 1)\)\ Exp[\(-z\)\ r/ n]\ Hypergeometric1F1[l + 1 - n, 2\ l + 2, 2\ z\ r/n]\)], "Input"], Cell[BoxData[ \(\(\(1\/\(n\ \(\((1 + 2\ l)\)!\)\)\)\((2\^\(1 + l\)\ \[ExponentialE]\^\(-\(\(r\ z\)\ \/n\)\)\ \((\(r\ z\)\/n)\)\^\(1 + l\)\ \@\(\(z\ \(\((l + n)\)!\)\)\/\(\((\(-1\ \) - l + n)\)!\)\)\ Hypergeometric1F1[1 + l - n, 2 + 2\ l, \(2\ r\ z\)\/n])\)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(P10\ = \ Coul[1, 0, Z, r]\)\(\[IndentingNewLine]\) \)\)], "Input"], Cell[BoxData[ \(2\ \[ExponentialE]\^\(\(-r\)\ Z\)\ r\ Z\^\(3/2\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(Do[ Print[StringForm["\", n, l, Coul[n, l, Z, r]]], {l, 0, 4}, {n, l + 1, 5}]\)\(\[IndentingNewLine]\) \)\)], "Input"], Cell[BoxData[ InterpretationBox["\<\"P[\\!\\(1\\),\\!\\(0\\)](r) = \\!\\(2\\\\ \ \[ExponentialE]\\^\\(\\(\\(-r\\)\\)\\\\ Z\\)\\\\ r\\\\ Z\\^\\(3/2\\)\\)\"\>", StringForm[ "P[``,``](r) = ``", 1, 0, Times[ 2, Power[ E, Times[ -1, r, Z]], r, Power[ Z, Rational[ 3, 2]]]], Editable->False]], "Print"], Cell[BoxData[ InterpretationBox["\<\"P[\\!\\(2\\),\\!\\(0\\)](r) = \\!\\(\\(\ \[ExponentialE]\\^\\(-\\(\\(\\(r\\\\ Z\\)\\/2\\)\\)\\)\\\\ r\\\\ \ Z\\^\\(3/2\\)\\\\ \\(\\((1 - \\(r\\\\ Z\\)\\/2)\\)\\)\\)\\/\\@2\\)\"\>", StringForm[ "P[``,``](r) = ``", 2, 0, Times[ Power[ 2, Rational[ -1, 2]], Power[ E, Times[ Rational[ -1, 2], r, Z]], r, Power[ Z, Rational[ 3, 2]], Plus[ 1, Times[ Rational[ -1, 2], r, Z]]]], Editable->False]], "Print"], Cell[BoxData[ InterpretationBox["\<\"P[\\!\\(3\\),\\!\\(0\\)](r) = \\!\\(\\(2\\\\ \ \[ExponentialE]\\^\\(-\\(\\(\\(r\\\\ Z\\)\\/3\\)\\)\\)\\\\ r\\\\ \ Z\\^\\(3/2\\)\\\\ \\(\\((1 - \\(2\\\\ r\\\\ Z\\)\\/3 + \\(2\\\\ r\\^2\\\\ \ Z\\^2\\)\\/27)\\)\\)\\)\\/\\(3\\\\ \\@3\\)\\)\"\>", StringForm[ "P[``,``](r) = ``", 3, 0, Times[ Rational[ 2, 3], Power[ 3, Rational[ -1, 2]], Power[ E, Times[ Rational[ -1, 3], r, Z]], r, Power[ Z, Rational[ 3, 2]], Plus[ 1, Times[ Rational[ -2, 3], r, Z], Times[ Rational[ 2, 27], Power[ r, 2], Power[ Z, 2]]]]], Editable->False]], "Print"], Cell[BoxData[ InterpretationBox["\<\"P[\\!\\(4\\),\\!\\(0\\)](r) = \\!\\(1\\/4\\\\ \ \[ExponentialE]\\^\\(-\\(\\(\\(r\\\\ Z\\)\\/4\\)\\)\\)\\\\ r\\\\ \ 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r, Z], Times[ Rational[ 4, 25], Power[ r, 2], Power[ Z, 2]], Times[ Rational[ -4, 375], Power[ r, 3], Power[ Z, 3]], Times[ Rational[ 2, 9375], Power[ r, 4], Power[ Z, 4]]]]], Editable->False]], "Print"], Cell[BoxData[ InterpretationBox["\<\"P[\\!\\(2\\),\\!\\(1\\)](r) = \\!\\(\\(\ \[ExponentialE]\\^\\(-\\(\\(\\(r\\\\ Z\\)\\/2\\)\\)\\)\\\\ r\\^2\\\\ \ Z\\^\\(5/2\\)\\)\\/\\(2\\\\ \\@6\\)\\)\"\>", StringForm[ "P[``,``](r) = ``", 2, 1, Times[ Rational[ 1, 2], Power[ 6, Rational[ -1, 2]], Power[ E, Times[ Rational[ -1, 2], r, Z]], Power[ r, 2], Power[ Z, Rational[ 5, 2]]]], Editable->False]], "Print"], Cell[BoxData[ InterpretationBox["\<\"P[\\!\\(3\\),\\!\\(1\\)](r) = \\!\\(4\\/27\\\\ \\@\ \\(2\\/3\\)\\\\ \[ExponentialE]\\^\\(-\\(\\(\\(r\\\\ Z\\)\\/3\\)\\)\\)\\\\ \ r\\^2\\\\ Z\\^\\(5/2\\)\\\\ \\(\\((1 - \\(r\\\\ Z\\)\\/6)\\)\\)\\)\"\>", StringForm[ "P[``,``](r) = ``", 3, 1, Times[ Rational[ 4, 27], Power[ Rational[ 2, 3], Rational[ 1, 2]], Power[ E, Times[ Rational[ -1, 3], r, Z]], Power[ 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