mirror of
https://asciireactor.com/otho/phy-520.git
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1771 lines
70 KiB
Mathematica
1771 lines
70 KiB
Mathematica
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LaguerreL[$CellContext`n - $CellContext`L - 1, 2 $CellContext`L +
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" are the spherical harmonics and the radial functions are ",
|
||
|
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||
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RowBox[{
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||
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SqrtBox[
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FractionBox[
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RowBox[{"n", "-", "1", "-", "\[ScriptL]"}], ")"}], "!"}],
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||
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RowBox[{"2", " ",
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||
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SuperscriptBox[
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||
|
RowBox[{"n", " ", "[",
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RowBox[{
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RowBox[{"(",
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SuperscriptBox[
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||
|
RowBox[{"(",
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||
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FractionBox["2",
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RowBox[{"n", " ",
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SubscriptBox["a", "0"]}]], ")"}],
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RowBox[{"\[ScriptL]", "+",
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RowBox[{"3", "/", "2"}]}]],
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SuperscriptBox["r", "\[ScriptL]"],
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||
|
SuperscriptBox["e",
|
||
|
RowBox[{
|
||
|
RowBox[{
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||
|
RowBox[{"-", "r"}], "/", "n"}], " ",
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||
|
SubscriptBox["a", "0"]}]],
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||
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RowBox[{
|
||
|
SubsuperscriptBox["L",
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||
|
RowBox[{"n", "+", "\[ScriptL]"}],
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||
|
RowBox[{
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||
|
RowBox[{"2", " ", "\[ScriptL]"}], "+", "1"}]], "(",
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||
|
RowBox[{"2", " ",
|
||
|
RowBox[{"r", "/", "n"}], " ",
|
||
|
SubscriptBox["a", "0"]}], ")"}]}]}], TraditionalForm]], "InlineMath"],
|
||
|
", where ",
|
||
|
Cell[BoxData[
|
||
|
FormBox[
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||
|
RowBox[{
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||
|
SubsuperscriptBox["L", "p", "a"], "(", "x", ")"}], TraditionalForm]],
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||
|
"InlineMath"],
|
||
|
" is the ",
|
||
|
Cell[BoxData[
|
||
|
FormBox[
|
||
|
SuperscriptBox["p", "th"], TraditionalForm]], "InlineMath"],
|
||
|
"-order associated Laguerre polynomial and ",
|
||
|
Cell[BoxData[
|
||
|
FormBox[
|
||
|
SubscriptBox["a", "0"], TraditionalForm]], "InlineMath"],
|
||
|
" is the Bohr radius. The left graphic shows the radial probability density ",
|
||
|
Cell[BoxData[
|
||
|
FormBox[
|
||
|
RowBox[{
|
||
|
SuperscriptBox["r", "2"], "|",
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||
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RowBox[{
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||
|
SubscriptBox["R",
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||
|
RowBox[{"n", ",", "\[ScriptL]"}]], "(", "r", ")"}],
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||
|
SuperscriptBox["|", "2"]}], TraditionalForm]], "InlineMath"],
|
||
|
" and the expectation value ",
|
||
|
Cell[BoxData[
|
||
|
FormBox[
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||
|
RowBox[{
|
||
|
RowBox[{
|
||
|
SubscriptBox[
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||
|
RowBox[{"\[LeftAngleBracket]", "r", "\[RightAngleBracket]"}],
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||
|
RowBox[{"n", ",", "\[ScriptL]"}]], "\[Congruent]",
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||
|
RowBox[{"\[LeftAngleBracket]",
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||
|
RowBox[{
|
||
|
SubscriptBox["\[Phi]",
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||
|
RowBox[{"n", ",",
|
||
|
RowBox[{"\[ScriptL]", ".", "m"}]}]], "|", "r", "|",
|
||
|
SubscriptBox["\[Phi]",
|
||
|
RowBox[{"n", ",",
|
||
|
RowBox[{"\[ScriptL]", ".", "m"}]}]]}], "\[RightAngleBracket]"}]}],
|
||
|
"=",
|
||
|
RowBox[{
|
||
|
SuperscriptBox["n", "2"],
|
||
|
RowBox[{
|
||
|
SubscriptBox["a", "0"], "[",
|
||
|
RowBox[{"1", "+",
|
||
|
RowBox[{
|
||
|
FractionBox["1", "2"],
|
||
|
RowBox[{"(",
|
||
|
RowBox[{"1", "-",
|
||
|
FractionBox[
|
||
|
RowBox[{"\[ScriptL]", "(",
|
||
|
RowBox[{"\[ScriptL]", "+", "1"}], ")"}],
|
||
|
SuperscriptBox["n", "2"]]}], ")"}]}]}], "]"}]}]}],
|
||
|
TraditionalForm]], "InlineMath"],
|
||
|
", and the right graphic shows the radial function."
|
||
|
}], "ManipulateCaption",
|
||
|
CellChangeTimes->{
|
||
|
3.35696210375764*^9, {3.471529068929021*^9, 3.4715293165026093`*^9}, {
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||
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3.4715293831639*^9, 3.471529437061977*^9}, {3.4715295487840357`*^9,
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||
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3.47152981401045*^9}, {3.47152985069398*^9, 3.4715298662521133`*^9}, {
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||
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3.471789183048913*^9, 3.471789183048913*^9}, {3.471789525117981*^9,
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||
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3.4717895308993416`*^9}, {3.4717895892285867`*^9,
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||
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3.4717898109047174`*^9}, {3.471814078224716*^9, 3.4718140791921043`*^9}, {
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||
|
3.4718889185129423`*^9, 3.471888972939502*^9}},
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||
|
CellID->47933019]
|
||
|
}, Open ]],
|
||
|
|
||
|
Cell[CellGroupData[{
|
||
|
|
||
|
Cell["", "ThumbnailSection"],
|
||
|
|
||
|
Cell[BoxData[
|
||
|
TagBox[
|
||
|
StyleBox[
|
||
|
DynamicModuleBox[{$CellContext`L$$ = 2, $CellContext`n$$ = 3,
|
||
|
Typeset`show$$ = True, Typeset`bookmarkList$$ = {},
|
||
|
Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ =
|
||
|
1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{
|
||
|
Hold[$CellContext`n$$], 3, "quantum numbers n"}, {1, 2, 3, 4}}, {{
|
||
|
Hold[$CellContext`L$$], 2,
|
||
|
Style["l", Italic]},
|
||
|
Dynamic[
|
||
|
Range[0, $CellContext`n$$ - 1]]}}, Typeset`size$$ = {
|
||
|
600., {147., 153.}}, Typeset`update$$ = 0, Typeset`initDone$$,
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||
|
Typeset`skipInitDone$$ = False, $CellContext`n$69255$$ = 0},
|
||
|
DynamicBox[Manipulate`ManipulateBoxes[
|
||
|
1, StandardForm,
|
||
|
"Variables" :> {$CellContext`L$$ = 2, $CellContext`n$$ = 3},
|
||
|
"ControllerVariables" :> {
|
||
|
Hold[$CellContext`n$$, $CellContext`n$69255$$, 0]},
|
||
|
"OtherVariables" :> {
|
||
|
Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$,
|
||
|
Typeset`animator$$, Typeset`animvar$$, Typeset`name$$,
|
||
|
Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
|
||
|
Typeset`skipInitDone$$},
|
||
|
"Body" :> (
|
||
|
If[$CellContext`L$$ >= $CellContext`n$$, $CellContext`L$$ = \
|
||
|
$CellContext`n$$ - 1]; $CellContext`label = Which[$CellContext`L$$ == 0,
|
||
|
Style["s", Italic], $CellContext`L$$ == 1,
|
||
|
Style["p", Italic], $CellContext`L$$ == 2,
|
||
|
Style["d", Italic], $CellContext`L$$ == 3,
|
||
|
Style["f", Italic]]; $CellContext`p1 = Quiet[
|
||
|
|
||
|
Plot[$CellContext`r^2 $CellContext`R[$CellContext`n$$, \
|
||
|
$CellContext`L$$, $CellContext`r]^2, {$CellContext`r, 0,
|
||
|
Part[$CellContext`rmax, $CellContext`n$$]}, PlotRange -> {{0,
|
||
|
Part[$CellContext`rmax, $CellContext`n$$]}, {0,
|
||
|
Part[$CellContext`yrange, $CellContext`n$$]}}, Filling -> Axis,
|
||
|
Ticks -> Part[$CellContext`ticksmat, $CellContext`n$$, 1],
|
||
|
TicksStyle -> Directive[16, Gray], PlotStyle -> Thick, PlotLabel ->
|
||
|
Style[
|
||
|
Row[{
|
||
|
NumberForm[$CellContext`n$$, 1], $CellContext`label}], 18,
|
||
|
Darker[Blue]],
|
||
|
AxesLabel -> $CellContext`label1]]; $CellContext`av =
|
||
|
Graphics[{Thick, Dashed, Blue,
|
||
|
Line[{{
|
||
|
$CellContext`rav[$CellContext`n$$, $CellContext`L$$], 0}, {
|
||
|
$CellContext`rav[$CellContext`n$$, $CellContext`L$$],
|
||
|
Part[$CellContext`yrange, $CellContext`n$$]}}],
|
||
|
Text[
|
||
|
Style[
|
||
|
Row[{"\[LeftAngleBracket]",
|
||
|
Style["r", Italic],
|
||
|
"\!\(\*SubscriptBox[\(\[RightAngleBracket]\), \(n, l\)]\)"}],
|
||
|
18], {1.48 $CellContext`rav[$CellContext`n$$, $CellContext`L$$],
|
||
|
0.8 Part[$CellContext`yrange, $CellContext`n$$]}]}]; Pane[
|
||
|
If[$CellContext`L$$ < $CellContext`n$$,
|
||
|
GraphicsRow[{
|
||
|
Show[$CellContext`p1, $CellContext`av],
|
||
|
Plot[
|
||
|
$CellContext`R[$CellContext`n$$, $CellContext`L$$, \
|
||
|
$CellContext`r], {$CellContext`r, 0,
|
||
|
Part[$CellContext`rmax, $CellContext`n$$]}, PlotRange -> All,
|
||
|
Ticks -> Part[$CellContext`ticksmat, $CellContext`n$$, 2],
|
||
|
TicksStyle -> Directive[16, Gray], PlotStyle -> Thick,
|
||
|
AxesLabel -> $CellContext`label2]}, ImageSize -> {600, 300}],
|
||
|
Null], ImageSize -> {600, 300}]),
|
||
|
"Specifications" :> {{{$CellContext`n$$, 3, "quantum numbers n"}, {1,
|
||
|
2, 3, 4}}, {{$CellContext`L$$, 2,
|
||
|
Style["l", Italic]},
|
||
|
Dynamic[
|
||
|
Range[0, $CellContext`n$$ - 1]]}},
|
||
|
"Options" :> {
|
||
|
ControlType -> SetterBar,
|
||
|
TrackedSymbols :> {$CellContext`n$$, $CellContext`L$$}},
|
||
|
"DefaultOptions" :> {ControllerLinking -> True}],
|
||
|
ImageSizeCache->{643., {202., 207.}},
|
||
|
SingleEvaluation->True],
|
||
|
Deinitialization:>None,
|
||
|
DynamicModuleValues:>{},
|
||
|
Initialization:>(($CellContext`F[
|
||
|
Pattern[$CellContext`n,
|
||
|
Blank[]],
|
||
|
Pattern[$CellContext`L,
|
||
|
Blank[]],
|
||
|
Pattern[$CellContext`x,
|
||
|
Blank[]]] := (($CellContext`x^$CellContext`L
|
||
|
E^((-$CellContext`x)/2)) Factorial[$CellContext`n + $CellContext`L])
|
||
|
LaguerreL[$CellContext`n - $CellContext`L - 1, 2 $CellContext`L +
|
||
|
1, $CellContext`x]; $CellContext`R[
|
||
|
Pattern[$CellContext`n,
|
||
|
Blank[]],
|
||
|
Pattern[$CellContext`L,
|
||
|
Blank[]],
|
||
|
Pattern[$CellContext`r,
|
||
|
|
||
|
Blank[]]] := (($CellContext`a^((-3)/2) (2/$CellContext`n^2)) (
|
||
|
Factorial[$CellContext`n - 1 - $CellContext`L]/
|
||
|
Factorial[$CellContext`n + $CellContext`L]^3)^
|
||
|
Rational[1, 2]) $CellContext`F[$CellContext`n, $CellContext`L,
|
||
|
2 ($CellContext`r/($CellContext`n $CellContext`a))]; \
|
||
|
$CellContext`rav[
|
||
|
Pattern[$CellContext`np,
|
||
|
Blank[]],
|
||
|
Pattern[$CellContext`Lp,
|
||
|
Blank[]]] := $CellContext`np^2 (1. +
|
||
|
0.5 (1. - $CellContext`Lp (($CellContext`Lp +
|
||
|
1.)/$CellContext`np^2))); $CellContext`a =
|
||
|
1; $CellContext`rmax = {5, 15, 30, 50, 70}; $CellContext`yrange = {
|
||
|
0.55, 0.2, 0.12, 0.07}; $CellContext`ticksmat =
|
||
|
ConstantArray[0., {5, 2}];
|
||
|
Part[$CellContext`ticksmat, 1, 1] = {{0, 2, 4}, {0.25, 0.5}};
|
||
|
Part[$CellContext`ticksmat, 1, 2] = {{0, 2, 4}, Automatic};
|
||
|
Part[$CellContext`ticksmat, 2, 1] = {{0, 6, 12}, {0.05, 0.15}};
|
||
|
Part[$CellContext`ticksmat, 2, 2] = {{0, 6, 12}, Automatic};
|
||
|
Part[$CellContext`ticksmat, 3, 1] = {{0, 10, 20}, {0.05, 0.1}};
|
||
|
Part[$CellContext`ticksmat, 3, 2] = {{0, 10, 20}, Automatic};
|
||
|
Part[$CellContext`ticksmat, 4, 1] = {{0, 20, 40}, {0.03, 0.06}};
|
||
|
Part[$CellContext`ticksmat, 4, 2] = {{0, 20, 40},
|
||
|
Automatic}; $CellContext`label1 = {
|
||
|
Text[
|
||
|
Style[
|
||
|
Row[{
|
||
|
Style["r", Italic], " / ",
|
||
|
Subscript[
|
||
|
Style["a", Italic], 0]}], 18]],
|
||
|
Text[
|
||
|
Style[
|
||
|
Row[{Style["r", Italic]^2, " ",
|
||
|
Subscript[
|
||
|
Style["R", Italic],
|
||
|
Row[{
|
||
|
Style["n", Italic], ", ",
|
||
|
Style["l", Italic]}]], "(",
|
||
|
Style["r", Italic], ")"^2}], 18]]}; $CellContext`label2 = {
|
||
|
Text[
|
||
|
Style[
|
||
|
Row[{
|
||
|
Style["r", Italic], " / ",
|
||
|
Subscript[
|
||
|
Style["a", Italic], 0]}], 18]],
|
||
|
Text[
|
||
|
Style[
|
||
|
Row[{
|
||
|
Subscript[
|
||
|
Style["R", Italic],
|
||
|
Row[{
|
||
|
Style["n", Italic], ", ",
|
||
|
Style["l", Italic]}]], "(",
|
||
|
Style["r", Italic], ")"}], 18]]}); Typeset`initDone$$ = True),
|
||
|
SynchronousInitialization->True,
|
||
|
UnsavedVariables:>{Typeset`initDone$$},
|
||
|
UntrackedVariables:>{Typeset`size$$}], "Manipulate",
|
||
|
Deployed->True,
|
||
|
StripOnInput->False],
|
||
|
Manipulate`InterpretManipulate[1]]], "Output",
|
||
|
CellID->1957055702]
|
||
|
}, Open ]],
|
||
|
|
||
|
Cell[CellGroupData[{
|
||
|
|
||
|
Cell["", "SnapshotsSection"],
|
||
|
|
||
|
Cell[BoxData[
|
||
|
TagBox[
|
||
|
StyleBox[
|
||
|
DynamicModuleBox[{$CellContext`L$$ = 1, $CellContext`n$$ = 3,
|
||
|
Typeset`show$$ = True, Typeset`bookmarkList$$ = {},
|
||
|
Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ =
|
||
|
1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{
|
||
|
Hold[$CellContext`n$$], 3, "quantum numbers n"}, {1, 2, 3, 4}}, {{
|
||
|
Hold[$CellContext`L$$], 1,
|
||
|
Style["l", Italic]},
|
||
|
Dynamic[
|
||
|
Range[0, $CellContext`n$$ - 1]]}}, Typeset`size$$ = {
|
||
|
600., {147., 153.}}, Typeset`update$$ = 0, Typeset`initDone$$,
|
||
|
Typeset`skipInitDone$$ = False, $CellContext`n$69306$$ = 0},
|
||
|
DynamicBox[Manipulate`ManipulateBoxes[
|
||
|
1, StandardForm,
|
||
|
"Variables" :> {$CellContext`L$$ = 1, $CellContext`n$$ = 3},
|
||
|
"ControllerVariables" :> {
|
||
|
Hold[$CellContext`n$$, $CellContext`n$69306$$, 0]},
|
||
|
"OtherVariables" :> {
|
||
|
Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$,
|
||
|
Typeset`animator$$, Typeset`animvar$$, Typeset`name$$,
|
||
|
Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
|
||
|
Typeset`skipInitDone$$},
|
||
|
"Body" :> (
|
||
|
If[$CellContext`L$$ >= $CellContext`n$$, $CellContext`L$$ = \
|
||
|
$CellContext`n$$ - 1]; $CellContext`label = Which[$CellContext`L$$ == 0,
|
||
|
Style["s", Italic], $CellContext`L$$ == 1,
|
||
|
Style["p", Italic], $CellContext`L$$ == 2,
|
||
|
Style["d", Italic], $CellContext`L$$ == 3,
|
||
|
Style["f", Italic]]; $CellContext`p1 = Quiet[
|
||
|
|
||
|
Plot[$CellContext`r^2 $CellContext`R[$CellContext`n$$, \
|
||
|
$CellContext`L$$, $CellContext`r]^2, {$CellContext`r, 0,
|
||
|
Part[$CellContext`rmax, $CellContext`n$$]}, PlotRange -> {{0,
|
||
|
Part[$CellContext`rmax, $CellContext`n$$]}, {0,
|
||
|
Part[$CellContext`yrange, $CellContext`n$$]}}, Filling -> Axis,
|
||
|
Ticks -> Part[$CellContext`ticksmat, $CellContext`n$$, 1],
|
||
|
TicksStyle -> Directive[16, Gray], PlotStyle -> Thick, PlotLabel ->
|
||
|
Style[
|
||
|
Row[{
|
||
|
NumberForm[$CellContext`n$$, 1], $CellContext`label}], 18,
|
||
|
Darker[Blue]],
|
||
|
AxesLabel -> $CellContext`label1]]; $CellContext`av =
|
||
|
Graphics[{Thick, Dashed, Blue,
|
||
|
Line[{{
|
||
|
$CellContext`rav[$CellContext`n$$, $CellContext`L$$], 0}, {
|
||
|
$CellContext`rav[$CellContext`n$$, $CellContext`L$$],
|
||
|
Part[$CellContext`yrange, $CellContext`n$$]}}],
|
||
|
Text[
|
||
|
Style[
|
||
|
Row[{"\[LeftAngleBracket]",
|
||
|
Style["r", Italic],
|
||
|
"\!\(\*SubscriptBox[\(\[RightAngleBracket]\), \(n, l\)]\)"}],
|
||
|
18], {1.48 $CellContext`rav[$CellContext`n$$, $CellContext`L$$],
|
||
|
0.8 Part[$CellContext`yrange, $CellContext`n$$]}]}]; Pane[
|
||
|
If[$CellContext`L$$ < $CellContext`n$$,
|
||
|
GraphicsRow[{
|
||
|
Show[$CellContext`p1, $CellContext`av],
|
||
|
Plot[
|
||
|
$CellContext`R[$CellContext`n$$, $CellContext`L$$, \
|
||
|
$CellContext`r], {$CellContext`r, 0,
|
||
|
Part[$CellContext`rmax, $CellContext`n$$]}, PlotRange -> All,
|
||
|
Ticks -> Part[$CellContext`ticksmat, $CellContext`n$$, 2],
|
||
|
TicksStyle -> Directive[16, Gray], PlotStyle -> Thick,
|
||
|
AxesLabel -> $CellContext`label2]}, ImageSize -> {600, 300}],
|
||
|
Null], ImageSize -> {600, 300}]),
|
||
|
"Specifications" :> {{{$CellContext`n$$, 3, "quantum numbers n"}, {1,
|
||
|
2, 3, 4}}, {{$CellContext`L$$, 1,
|
||
|
Style["l", Italic]},
|
||
|
Dynamic[
|
||
|
Range[0, $CellContext`n$$ - 1]]}},
|
||
|
"Options" :> {
|
||
|
ControlType -> SetterBar,
|
||
|
TrackedSymbols :> {$CellContext`n$$, $CellContext`L$$}},
|
||
|
"DefaultOptions" :> {ControllerLinking -> True}],
|
||
|
ImageSizeCache->{643., {202., 207.}},
|
||
|
SingleEvaluation->True],
|
||
|
Deinitialization:>None,
|
||
|
DynamicModuleValues:>{},
|
||
|
Initialization:>(($CellContext`F[
|
||
|
Pattern[$CellContext`n,
|
||
|
Blank[]],
|
||
|
Pattern[$CellContext`L,
|
||
|
Blank[]],
|
||
|
Pattern[$CellContext`x,
|
||
|
Blank[]]] := (($CellContext`x^$CellContext`L
|
||
|
E^((-$CellContext`x)/2)) Factorial[$CellContext`n + $CellContext`L])
|
||
|
LaguerreL[$CellContext`n - $CellContext`L - 1, 2 $CellContext`L +
|
||
|
1, $CellContext`x]; $CellContext`R[
|
||
|
Pattern[$CellContext`n,
|
||
|
Blank[]],
|
||
|
Pattern[$CellContext`L,
|
||
|
Blank[]],
|
||
|
Pattern[$CellContext`r,
|
||
|
|
||
|
Blank[]]] := (($CellContext`a^((-3)/2) (2/$CellContext`n^2)) (
|
||
|
Factorial[$CellContext`n - 1 - $CellContext`L]/
|
||
|
Factorial[$CellContext`n + $CellContext`L]^3)^
|
||
|
Rational[1, 2]) $CellContext`F[$CellContext`n, $CellContext`L,
|
||
|
2 ($CellContext`r/($CellContext`n $CellContext`a))]; \
|
||
|
$CellContext`rav[
|
||
|
Pattern[$CellContext`np,
|
||
|
Blank[]],
|
||
|
Pattern[$CellContext`Lp,
|
||
|
Blank[]]] := $CellContext`np^2 (1. +
|
||
|
0.5 (1. - $CellContext`Lp (($CellContext`Lp +
|
||
|
1.)/$CellContext`np^2))); $CellContext`a =
|
||
|
1; $CellContext`rmax = {5, 15, 30, 50, 70}; $CellContext`yrange = {
|
||
|
0.55, 0.2, 0.12, 0.07}; $CellContext`ticksmat =
|
||
|
ConstantArray[0., {5, 2}];
|
||
|
Part[$CellContext`ticksmat, 1, 1] = {{0, 2, 4}, {0.25, 0.5}};
|
||
|
Part[$CellContext`ticksmat, 1, 2] = {{0, 2, 4}, Automatic};
|
||
|
Part[$CellContext`ticksmat, 2, 1] = {{0, 6, 12}, {0.05, 0.15}};
|
||
|
Part[$CellContext`ticksmat, 2, 2] = {{0, 6, 12}, Automatic};
|
||
|
Part[$CellContext`ticksmat, 3, 1] = {{0, 10, 20}, {0.05, 0.1}};
|
||
|
Part[$CellContext`ticksmat, 3, 2] = {{0, 10, 20}, Automatic};
|
||
|
Part[$CellContext`ticksmat, 4, 1] = {{0, 20, 40}, {0.03, 0.06}};
|
||
|
Part[$CellContext`ticksmat, 4, 2] = {{0, 20, 40},
|
||
|
Automatic}; $CellContext`label1 = {
|
||
|
Text[
|
||
|
Style[
|
||
|
Row[{
|
||
|
Style["r", Italic], " / ",
|
||
|
Subscript[
|
||
|
Style["a", Italic], 0]}], 18]],
|
||
|
Text[
|
||
|
Style[
|
||
|
Row[{Style["r", Italic]^2, " ",
|
||
|
Subscript[
|
||
|
Style["R", Italic],
|
||
|
Row[{
|
||
|
Style["n", Italic], ", ",
|
||
|
Style["l", Italic]}]], "(",
|
||
|
Style["r", Italic], ")"^2}], 18]]}; $CellContext`label2 = {
|
||
|
Text[
|
||
|
Style[
|
||
|
Row[{
|
||
|
Style["r", Italic], " / ",
|
||
|
Subscript[
|
||
|
Style["a", Italic], 0]}], 18]],
|
||
|
Text[
|
||
|
Style[
|
||
|
Row[{
|
||
|
Subscript[
|
||
|
Style["R", Italic],
|
||
|
Row[{
|
||
|
Style["n", Italic], ", ",
|
||
|
Style["l", Italic]}]], "(",
|
||
|
Style["r", Italic], ")"}], 18]]}); Typeset`initDone$$ = True),
|
||
|
SynchronousInitialization->True,
|
||
|
UnsavedVariables:>{Typeset`initDone$$},
|
||
|
UntrackedVariables:>{Typeset`size$$}], "Manipulate",
|
||
|
Deployed->True,
|
||
|
StripOnInput->False],
|
||
|
Manipulate`InterpretManipulate[1]]], "Output",
|
||
|
CellID->1375646062],
|
||
|
|
||
|
Cell[BoxData[
|
||
|
TagBox[
|
||
|
StyleBox[
|
||
|
DynamicModuleBox[{$CellContext`L$$ = 3, $CellContext`n$$ = 4,
|
||
|
Typeset`show$$ = True, Typeset`bookmarkList$$ = {},
|
||
|
Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ =
|
||
|
1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{
|
||
|
Hold[$CellContext`n$$], 4, "quantum numbers n"}, {1, 2, 3, 4}}, {{
|
||
|
Hold[$CellContext`L$$], 3,
|
||
|
Style["l", Italic]},
|
||
|
Dynamic[
|
||
|
Range[0, $CellContext`n$$ - 1]]}}, Typeset`size$$ = {
|
||
|
600., {147., 153.}}, Typeset`update$$ = 0, Typeset`initDone$$,
|
||
|
Typeset`skipInitDone$$ = False, $CellContext`n$69357$$ = 0},
|
||
|
DynamicBox[Manipulate`ManipulateBoxes[
|
||
|
1, StandardForm,
|
||
|
"Variables" :> {$CellContext`L$$ = 3, $CellContext`n$$ = 4},
|
||
|
"ControllerVariables" :> {
|
||
|
Hold[$CellContext`n$$, $CellContext`n$69357$$, 0]},
|
||
|
"OtherVariables" :> {
|
||
|
Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$,
|
||
|
Typeset`animator$$, Typeset`animvar$$, Typeset`name$$,
|
||
|
Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
|
||
|
Typeset`skipInitDone$$},
|
||
|
"Body" :> (
|
||
|
If[$CellContext`L$$ >= $CellContext`n$$, $CellContext`L$$ = \
|
||
|
$CellContext`n$$ - 1]; $CellContext`label = Which[$CellContext`L$$ == 0,
|
||
|
Style["s", Italic], $CellContext`L$$ == 1,
|
||
|
Style["p", Italic], $CellContext`L$$ == 2,
|
||
|
Style["d", Italic], $CellContext`L$$ == 3,
|
||
|
Style["f", Italic]]; $CellContext`p1 = Quiet[
|
||
|
|
||
|
Plot[$CellContext`r^2 $CellContext`R[$CellContext`n$$, \
|
||
|
$CellContext`L$$, $CellContext`r]^2, {$CellContext`r, 0,
|
||
|
Part[$CellContext`rmax, $CellContext`n$$]}, PlotRange -> {{0,
|
||
|
Part[$CellContext`rmax, $CellContext`n$$]}, {0,
|
||
|
Part[$CellContext`yrange, $CellContext`n$$]}}, Filling -> Axis,
|
||
|
Ticks -> Part[$CellContext`ticksmat, $CellContext`n$$, 1],
|
||
|
TicksStyle -> Directive[16, Gray], PlotStyle -> Thick, PlotLabel ->
|
||
|
Style[
|
||
|
Row[{
|
||
|
NumberForm[$CellContext`n$$, 1], $CellContext`label}], 18,
|
||
|
Darker[Blue]],
|
||
|
AxesLabel -> $CellContext`label1]]; $CellContext`av =
|
||
|
Graphics[{Thick, Dashed, Blue,
|
||
|
Line[{{
|
||
|
$CellContext`rav[$CellContext`n$$, $CellContext`L$$], 0}, {
|
||
|
$CellContext`rav[$CellContext`n$$, $CellContext`L$$],
|
||
|
Part[$CellContext`yrange, $CellContext`n$$]}}],
|
||
|
Text[
|
||
|
Style[
|
||
|
Row[{"\[LeftAngleBracket]",
|
||
|
Style["r", Italic],
|
||
|
"\!\(\*SubscriptBox[\(\[RightAngleBracket]\), \(n, l\)]\)"}],
|
||
|
18], {1.48 $CellContext`rav[$CellContext`n$$, $CellContext`L$$],
|
||
|
0.8 Part[$CellContext`yrange, $CellContext`n$$]}]}]; Pane[
|
||
|
If[$CellContext`L$$ < $CellContext`n$$,
|
||
|
GraphicsRow[{
|
||
|
Show[$CellContext`p1, $CellContext`av],
|
||
|
Plot[
|
||
|
$CellContext`R[$CellContext`n$$, $CellContext`L$$, \
|
||
|
$CellContext`r], {$CellContext`r, 0,
|
||
|
Part[$CellContext`rmax, $CellContext`n$$]}, PlotRange -> All,
|
||
|
Ticks -> Part[$CellContext`ticksmat, $CellContext`n$$, 2],
|
||
|
TicksStyle -> Directive[16, Gray], PlotStyle -> Thick,
|
||
|
AxesLabel -> $CellContext`label2]}, ImageSize -> {600, 300}],
|
||
|
Null], ImageSize -> {600, 300}]),
|
||
|
"Specifications" :> {{{$CellContext`n$$, 4, "quantum numbers n"}, {1,
|
||
|
2, 3, 4}}, {{$CellContext`L$$, 3,
|
||
|
Style["l", Italic]},
|
||
|
Dynamic[
|
||
|
Range[0, $CellContext`n$$ - 1]]}},
|
||
|
"Options" :> {
|
||
|
ControlType -> SetterBar,
|
||
|
TrackedSymbols :> {$CellContext`n$$, $CellContext`L$$}},
|
||
|
"DefaultOptions" :> {ControllerLinking -> True}],
|
||
|
ImageSizeCache->{643., {202., 207.}},
|
||
|
SingleEvaluation->True],
|
||
|
Deinitialization:>None,
|
||
|
DynamicModuleValues:>{},
|
||
|
Initialization:>(($CellContext`F[
|
||
|
Pattern[$CellContext`n,
|
||
|
Blank[]],
|
||
|
Pattern[$CellContext`L,
|
||
|
Blank[]],
|
||
|
Pattern[$CellContext`x,
|
||
|
Blank[]]] := (($CellContext`x^$CellContext`L
|
||
|
E^((-$CellContext`x)/2)) Factorial[$CellContext`n + $CellContext`L])
|
||
|
LaguerreL[$CellContext`n - $CellContext`L - 1, 2 $CellContext`L +
|
||
|
1, $CellContext`x]; $CellContext`R[
|
||
|
Pattern[$CellContext`n,
|
||
|
Blank[]],
|
||
|
Pattern[$CellContext`L,
|
||
|
Blank[]],
|
||
|
Pattern[$CellContext`r,
|
||
|
|
||
|
Blank[]]] := (($CellContext`a^((-3)/2) (2/$CellContext`n^2)) (
|
||
|
Factorial[$CellContext`n - 1 - $CellContext`L]/
|
||
|
Factorial[$CellContext`n + $CellContext`L]^3)^
|
||
|
Rational[1, 2]) $CellContext`F[$CellContext`n, $CellContext`L,
|
||
|
2 ($CellContext`r/($CellContext`n $CellContext`a))]; \
|
||
|
$CellContext`rav[
|
||
|
Pattern[$CellContext`np,
|
||
|
Blank[]],
|
||
|
Pattern[$CellContext`Lp,
|
||
|
Blank[]]] := $CellContext`np^2 (1. +
|
||
|
0.5 (1. - $CellContext`Lp (($CellContext`Lp +
|
||
|
1.)/$CellContext`np^2))); $CellContext`a =
|
||
|
1; $CellContext`rmax = {5, 15, 30, 50, 70}; $CellContext`yrange = {
|
||
|
0.55, 0.2, 0.12, 0.07}; $CellContext`ticksmat =
|
||
|
ConstantArray[0., {5, 2}];
|
||
|
Part[$CellContext`ticksmat, 1, 1] = {{0, 2, 4}, {0.25, 0.5}};
|
||
|
Part[$CellContext`ticksmat, 1, 2] = {{0, 2, 4}, Automatic};
|
||
|
Part[$CellContext`ticksmat, 2, 1] = {{0, 6, 12}, {0.05, 0.15}};
|
||
|
Part[$CellContext`ticksmat, 2, 2] = {{0, 6, 12}, Automatic};
|
||
|
Part[$CellContext`ticksmat, 3, 1] = {{0, 10, 20}, {0.05, 0.1}};
|
||
|
Part[$CellContext`ticksmat, 3, 2] = {{0, 10, 20}, Automatic};
|
||
|
Part[$CellContext`ticksmat, 4, 1] = {{0, 20, 40}, {0.03, 0.06}};
|
||
|
Part[$CellContext`ticksmat, 4, 2] = {{0, 20, 40},
|
||
|
Automatic}; $CellContext`label1 = {
|
||
|
Text[
|
||
|
Style[
|
||
|
Row[{
|
||
|
Style["r", Italic], " / ",
|
||
|
Subscript[
|
||
|
Style["a", Italic], 0]}], 18]],
|
||
|
Text[
|
||
|
Style[
|
||
|
Row[{Style["r", Italic]^2, " ",
|
||
|
Subscript[
|
||
|
Style["R", Italic],
|
||
|
Row[{
|
||
|
Style["n", Italic], ", ",
|
||
|
Style["l", Italic]}]], "(",
|
||
|
Style["r", Italic], ")"^2}], 18]]}; $CellContext`label2 = {
|
||
|
Text[
|
||
|
Style[
|
||
|
Row[{
|
||
|
Style["r", Italic], " / ",
|
||
|
Subscript[
|
||
|
Style["a", Italic], 0]}], 18]],
|
||
|
Text[
|
||
|
Style[
|
||
|
Row[{
|
||
|
Subscript[
|
||
|
Style["R", Italic],
|
||
|
Row[{
|
||
|
Style["n", Italic], ", ",
|
||
|
Style["l", Italic]}]], "(",
|
||
|
Style["r", Italic], ")"}], 18]]}); Typeset`initDone$$ = True),
|
||
|
SynchronousInitialization->True,
|
||
|
UnsavedVariables:>{Typeset`initDone$$},
|
||
|
UntrackedVariables:>{Typeset`size$$}], "Manipulate",
|
||
|
Deployed->True,
|
||
|
StripOnInput->False],
|
||
|
Manipulate`InterpretManipulate[1]]], "Output",
|
||
|
CellID->674420432],
|
||
|
|
||
|
Cell[BoxData[
|
||
|
TagBox[
|
||
|
StyleBox[
|
||
|
DynamicModuleBox[{$CellContext`L$$ = 2, $CellContext`n$$ = 3,
|
||
|
Typeset`show$$ = True, Typeset`bookmarkList$$ = {},
|
||
|
Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ =
|
||
|
1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{
|
||
|
Hold[$CellContext`n$$], 3, "quantum numbers n"}, {1, 2, 3, 4}}, {{
|
||
|
Hold[$CellContext`L$$], 2,
|
||
|
Style["l", Italic]},
|
||
|
Dynamic[
|
||
|
Range[0, $CellContext`n$$ - 1]]}}, Typeset`size$$ = {
|
||
|
600., {147., 153.}}, Typeset`update$$ = 0, Typeset`initDone$$,
|
||
|
Typeset`skipInitDone$$ = False, $CellContext`n$69408$$ = 0},
|
||
|
DynamicBox[Manipulate`ManipulateBoxes[
|
||
|
1, StandardForm,
|
||
|
"Variables" :> {$CellContext`L$$ = 2, $CellContext`n$$ = 3},
|
||
|
"ControllerVariables" :> {
|
||
|
Hold[$CellContext`n$$, $CellContext`n$69408$$, 0]},
|
||
|
"OtherVariables" :> {
|
||
|
Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$,
|
||
|
Typeset`animator$$, Typeset`animvar$$, Typeset`name$$,
|
||
|
Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
|
||
|
Typeset`skipInitDone$$},
|
||
|
"Body" :> (
|
||
|
If[$CellContext`L$$ >= $CellContext`n$$, $CellContext`L$$ = \
|
||
|
$CellContext`n$$ - 1]; $CellContext`label = Which[$CellContext`L$$ == 0,
|
||
|
Style["s", Italic], $CellContext`L$$ == 1,
|
||
|
Style["p", Italic], $CellContext`L$$ == 2,
|
||
|
Style["d", Italic], $CellContext`L$$ == 3,
|
||
|
Style["f", Italic]]; $CellContext`p1 = Quiet[
|
||
|
|
||
|
Plot[$CellContext`r^2 $CellContext`R[$CellContext`n$$, \
|
||
|
$CellContext`L$$, $CellContext`r]^2, {$CellContext`r, 0,
|
||
|
Part[$CellContext`rmax, $CellContext`n$$]}, PlotRange -> {{0,
|
||
|
Part[$CellContext`rmax, $CellContext`n$$]}, {0,
|
||
|
Part[$CellContext`yrange, $CellContext`n$$]}}, Filling -> Axis,
|
||
|
Ticks -> Part[$CellContext`ticksmat, $CellContext`n$$, 1],
|
||
|
TicksStyle -> Directive[16, Gray], PlotStyle -> Thick, PlotLabel ->
|
||
|
Style[
|
||
|
Row[{
|
||
|
NumberForm[$CellContext`n$$, 1], $CellContext`label}], 18,
|
||
|
Darker[Blue]],
|
||
|
AxesLabel -> $CellContext`label1]]; $CellContext`av =
|
||
|
Graphics[{Thick, Dashed, Blue,
|
||
|
Line[{{
|
||
|
$CellContext`rav[$CellContext`n$$, $CellContext`L$$], 0}, {
|
||
|
$CellContext`rav[$CellContext`n$$, $CellContext`L$$],
|
||
|
Part[$CellContext`yrange, $CellContext`n$$]}}],
|
||
|
Text[
|
||
|
Style[
|
||
|
Row[{"\[LeftAngleBracket]",
|
||
|
Style["r", Italic],
|
||
|
"\!\(\*SubscriptBox[\(\[RightAngleBracket]\), \(n, l\)]\)"}],
|
||
|
18], {1.48 $CellContext`rav[$CellContext`n$$, $CellContext`L$$],
|
||
|
0.8 Part[$CellContext`yrange, $CellContext`n$$]}]}]; Pane[
|
||
|
If[$CellContext`L$$ < $CellContext`n$$,
|
||
|
GraphicsRow[{
|
||
|
Show[$CellContext`p1, $CellContext`av],
|
||
|
Plot[
|
||
|
$CellContext`R[$CellContext`n$$, $CellContext`L$$, \
|
||
|
$CellContext`r], {$CellContext`r, 0,
|
||
|
Part[$CellContext`rmax, $CellContext`n$$]}, PlotRange -> All,
|
||
|
Ticks -> Part[$CellContext`ticksmat, $CellContext`n$$, 2],
|
||
|
TicksStyle -> Directive[16, Gray], PlotStyle -> Thick,
|
||
|
AxesLabel -> $CellContext`label2]}, ImageSize -> {600, 300}],
|
||
|
Null], ImageSize -> {600, 300}]),
|
||
|
"Specifications" :> {{{$CellContext`n$$, 3, "quantum numbers n"}, {1,
|
||
|
2, 3, 4}}, {{$CellContext`L$$, 2,
|
||
|
Style["l", Italic]},
|
||
|
Dynamic[
|
||
|
Range[0, $CellContext`n$$ - 1]]}},
|
||
|
"Options" :> {
|
||
|
ControlType -> SetterBar,
|
||
|
TrackedSymbols :> {$CellContext`n$$, $CellContext`L$$}},
|
||
|
"DefaultOptions" :> {ControllerLinking -> True}],
|
||
|
ImageSizeCache->{643., {202., 207.}},
|
||
|
SingleEvaluation->True],
|
||
|
Deinitialization:>None,
|
||
|
DynamicModuleValues:>{},
|
||
|
Initialization:>(($CellContext`F[
|
||
|
Pattern[$CellContext`n,
|
||
|
Blank[]],
|
||
|
Pattern[$CellContext`L,
|
||
|
Blank[]],
|
||
|
Pattern[$CellContext`x,
|
||
|
Blank[]]] := (($CellContext`x^$CellContext`L
|
||
|
E^((-$CellContext`x)/2)) Factorial[$CellContext`n + $CellContext`L])
|
||
|
LaguerreL[$CellContext`n - $CellContext`L - 1, 2 $CellContext`L +
|
||
|
1, $CellContext`x]; $CellContext`R[
|
||
|
Pattern[$CellContext`n,
|
||
|
Blank[]],
|
||
|
Pattern[$CellContext`L,
|
||
|
Blank[]],
|
||
|
Pattern[$CellContext`r,
|
||
|
|
||
|
Blank[]]] := (($CellContext`a^((-3)/2) (2/$CellContext`n^2)) (
|
||
|
Factorial[$CellContext`n - 1 - $CellContext`L]/
|
||
|
Factorial[$CellContext`n + $CellContext`L]^3)^
|
||
|
Rational[1, 2]) $CellContext`F[$CellContext`n, $CellContext`L,
|
||
|
2 ($CellContext`r/($CellContext`n $CellContext`a))]; \
|
||
|
$CellContext`rav[
|
||
|
Pattern[$CellContext`np,
|
||
|
Blank[]],
|
||
|
Pattern[$CellContext`Lp,
|
||
|
Blank[]]] := $CellContext`np^2 (1. +
|
||
|
0.5 (1. - $CellContext`Lp (($CellContext`Lp +
|
||
|
1.)/$CellContext`np^2))); $CellContext`a =
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1; $CellContext`rmax = {5, 15, 30, 50, 70}; $CellContext`yrange = {
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0.55, 0.2, 0.12, 0.07}; $CellContext`ticksmat =
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ConstantArray[0., {5, 2}];
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Part[$CellContext`ticksmat, 1, 1] = {{0, 2, 4}, {0.25, 0.5}};
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Part[$CellContext`ticksmat, 1, 2] = {{0, 2, 4}, Automatic};
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Part[$CellContext`ticksmat, 2, 1] = {{0, 6, 12}, {0.05, 0.15}};
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Part[$CellContext`ticksmat, 2, 2] = {{0, 6, 12}, Automatic};
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Part[$CellContext`ticksmat, 3, 1] = {{0, 10, 20}, {0.05, 0.1}};
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Part[$CellContext`ticksmat, 3, 2] = {{0, 10, 20}, Automatic};
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Part[$CellContext`ticksmat, 4, 1] = {{0, 20, 40}, {0.03, 0.06}};
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Part[$CellContext`ticksmat, 4, 2] = {{0, 20, 40},
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Automatic}; $CellContext`label1 = {
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Style[
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Row[{Style["r", Italic]^2, " ",
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Row[{
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Row[{
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Style["n", Italic], ", ",
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Style["l", Italic]}]], "(",
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Style["r", Italic], ")"}], 18]]}); Typeset`initDone$$ = True),
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|
SynchronousInitialization->True,
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|
UnsavedVariables:>{Typeset`initDone$$},
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|
UntrackedVariables:>{Typeset`size$$}], "Manipulate",
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Deployed->True,
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RowBox[{
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|
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FrameBox[
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GrayLevel[0.9]], "\" (or \"",
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FrameBox[
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|
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|
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FrameBox[
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FrameBox[
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GrayLevel[0.9]], "\" at the same time as \"",
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FrameBox[
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