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QNM-WKB3.mw
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QNM-WKB3.mw
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<?xml version="1.0" encoding="UTF-8"?>
<Worksheet>
<Version major="2022" minor="2"/>
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</View-Properties>
<MapleNet-Properties prettyprint="3" warnlevel="3" compactdisplay="false" preplot="" helpbrowser="standard" displayprecision="-1" echo="1" scientificx="true" unitattributes=""fontweight" = "bold"" imaginaryunit="I" longdelim="true" elisiontermsthreshold="10000" elisiondigitsafter="100" elisiondigitsbefore="100" plotdevice="inline" errorbreak="1" plotoptions="" plotdriver="opengl" quiet="false" elisiontermsbefore="100" elisiontermsafter="100" historytimestamp="false" screenwidth="79" indentamount="4" plotoutput="terminal" screenpixelheight="1200" rtablesize="[10, 10]" useclientjvm="true" format="document" labelwidth="20" postplot="" typesetting="extended" ansi="false" ansicolor="[]" elisiondigitsthreshold="10000" showassumed="1" ansilprint="false" trailingsemicolon="true" errorcursor="false" labelling="true" screenheight="25" prompt="> " verboseproc="1" latexwidth="8.0" ShowLabels="true"/>
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<Task-table>
<Task-category name="<default>"/>
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<Task/><Presentation-Block>
<Group view="code" labelreference="L3" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal"># Morris-Thorne's worm hole quasi-normal modes via the 3rd order WKB method</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L4" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">restart:</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L14" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">Digits := 20:</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L5" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal"># Physical parameters:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L6" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">L := 0: # angular momentum</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L7" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">s := 0: # spin parameter (0, 1, 2)</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L8" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">e := 1 - s^2:</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L9" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">n := 0: # QNM number</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L16" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">a := n + 1/2: a2 := a^2:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L10" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">V := x -> L*(L+1)/(1 + x^2) + e/(1 + x^2)^2:</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L12" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal"># Find the critical point:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L11" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">Eq := diff(V(x),x) = 0:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L13" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">x0 := fsolve(Eq, x=0): V0 := V(x0):</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L17" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">Vp2 := diff(V(x), x$2): V2 := evalf(subs(x=x0, Vp2)):</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L15" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">Vp3 := diff(V(x), x$3): V3 := evalf(subs(x=x0, Vp3)):</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L18" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">Vp4 := diff(V(x), x$4): V4 := evalf(subs(x=x0, Vp4)):</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L19" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">Vp5 := diff(V(x), x$5): V5 := evalf(subs(x=x0, Vp5)):</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L20" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">Vp6 := diff(V(x), x$6): V6 := evalf(subs(x=x0, Vp6)):</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L21" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">L2 := I/(8*sqrt(-2*V2))*(V4/V2*(1/4 + a2) - 1/36*(V3/V2)^2*(7 + 60*a2)):</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L24" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">L3 := a/(-2*V2)*(5/6912*(V3/V2)^4*(77 + 188*a2) - 1/384*(V3^2*V4/V2^3)*(51 + 100*a2) + 1/2304*(V4/V2)^2*(67 + 68*a2) + 1/288*(V3*V5/V2^2)*(19 + 28*a2) - 1/288*(V6/V2)*(5 + 4*a2)):</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L22" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">Omega := sqrt(V0 - I*sqrt(-2*V2)*(a + L2 + L3));</Text-field>
</Input>
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</Output>
</Group>
<Group view="presentation" inline-output="false" labelreference="L1" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
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</Worksheet>