UNPKG

mathmlben

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Visualization for goldstandard

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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="ModifyingAbove left-parenthesis normal upper Delta upper H right-parenthesis squared With bar equals StartFraction 1 Over upper N EndFraction sigma-summation Underscript i equals 1 Overscript upper N Endscripts left-bracket mathematical left-angle psi Subscript i Baseline StartAbsoluteValue upper H Subscript i Superscript 2 Baseline EndAbsoluteValue psi Subscript i Baseline mathematical right-angle minus mathematical left-angle psi Subscript i Baseline StartAbsoluteValue upper H Subscript i Baseline EndAbsoluteValue psi Subscript i Baseline mathematical right-angle squared right-bracket"> <semantics> <mrow data-semantic-type="relseq" data-semantic-role="equality" data-semantic-id="70" data-semantic-children="10,69" data-semantic-content="11"> <mrow class="MJX-TeXAtom-ORD"> <mover data-semantic-type="overscore" data-semantic-role="leftright" data-semantic-id="10" data-semantic-children="5,9" data-semantic-parent="70"> <mrow> <msup data-semantic-type="superscript" data-semantic-role="leftright" data-semantic-id="5" data-semantic-children="8,4" data-semantic-parent="10" data-semantic-fencepointer="3"> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="8" data-semantic-children="7" data-semantic-content="0,3" data-semantic-parent="5"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="0" data-semantic-parent="8">(</mo> <mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="7" data-semantic-children="1,2" data-semantic-content="6" data-semantic-parent="8"> <mi mathvariant="normal" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-id="1" data-semantic-parent="7">Δ <!-- Δ --> </mi> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="6" data-semantic-parent="7" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="2" data-semantic-parent="7">H</mi> </mrow> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="3" data-semantic-parent="8">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="4" data-semantic-parent="5">2</mn> </mrow> </msup> </mrow> <mo accent="false" data-semantic-type="operator" data-semantic-role="overaccent" data-semantic-id="9" data-semantic-parent="10">¯ <!-- ¯ --> </mo> </mover> </mrow> <mo data-semantic-type="relation" data-semantic-role="equality" data-semantic-id="11" data-semantic-parent="70" data-semantic-operator="relseq,=">=</mo> <mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="69" data-semantic-children="14,67" data-semantic-content="68" data-semantic-parent="70"> <mrow class="MJX-TeXAtom-ORD"> <mfrac data-semantic-type="fraction" data-semantic-role="division" data-semantic-id="14" data-semantic-children="12,13" data-semantic-parent="69"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="12" data-semantic-parent="14">1</mn> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="13" data-semantic-parent="14">N</mi> </mfrac> </mrow> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="68" data-semantic-parent="69" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <mrow data-semantic-type="bigop" data-semantic-role="sum" data-semantic-id="67" data-semantic-children="21,66" data-semantic-content="15" data-semantic-parent="69"> <munderover data-semantic-type="limboth" data-semantic-role="sum" data-semantic-id="21" data-semantic-children="15,19,20" data-semantic-parent="67"> <mo data-semantic-type="largeop" data-semantic-role="sum" data-semantic-id="15" data-semantic-parent="21" data-semantic-operator="bigop"><!-- ∑ --> </mo> <mrow class="MJX-TeXAtom-ORD" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-id="19" data-semantic-children="16,18" data-semantic-content="17" data-semantic-parent="21"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="16" data-semantic-parent="19">i</mi> <mo data-semantic-type="relation" data-semantic-role="equality" data-semantic-id="17" data-semantic-parent="19" data-semantic-operator="relseq,=">=</mo> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="18" data-semantic-parent="19">1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="20" data-semantic-parent="21">N</mi> </mrow> </munderover> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="66" data-semantic-children="65" data-semantic-content="22,54" data-semantic-parent="67"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="22" data-semantic-parent="66" data-semantic-operator="fenced">[</mo> <mrow data-semantic-type="infixop" data-semantic-role="subtraction" data-semantic-id="65" data-semantic-children="59,53" data-semantic-content="38" data-semantic-parent="66"> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="59" data-semantic-children="58" data-semantic-content="23,37" data-semantic-parent="65"> <mo fence="false" stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="23" data-semantic-parent="59" data-semantic-operator="fenced"><!-- ⟨ --> </mo> <mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="58" data-semantic-children="26,55,36" data-semantic-content="56,57" data-semantic-parent="59"> <msub data-semantic-type="subscript" data-semantic-role="greekletter" data-semantic-id="26" data-semantic-children="24,25" data-semantic-parent="58"> <mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="24" data-semantic-parent="26">ψ <!-- ψ --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="25" data-semantic-parent="26">i</mi> </mrow> </msub> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="56" data-semantic-parent="58" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <mrow data-semantic-type="fenced" data-semantic-role="neutral" data-semantic-id="55" data-semantic-children="32" data-semantic-content="27,33" data-semantic-parent="58"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="neutral" data-semantic-id="27" data-semantic-parent="55" data-semantic-operator="fenced">|</mo> </mrow> <msubsup data-semantic-type="subsup" data-semantic-role="latinletter" data-semantic-id="32" data-semantic-children="28,29,30" data-semantic-parent="55" data-semantic-collapsed="(32 (31 28 29) 30)"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="28" data-semantic-parent="32">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="29" data-semantic-parent="32">i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="30" data-semantic-parent="32">2</mn> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="neutral" data-semantic-id="33" data-semantic-parent="55" data-semantic-operator="fenced">|</mo> </mrow> </mrow> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="57" data-semantic-parent="58" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <msub data-semantic-type="subscript" data-semantic-role="greekletter" data-semantic-id="36" data-semantic-children="34,35" data-semantic-parent="58"> <mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="34" data-semantic-parent="36">ψ <!-- ψ --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="35" data-semantic-parent="36">i</mi> </mrow> </msub> </mrow> <mo fence="false" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="37" data-semantic-parent="59" data-semantic-operator="fenced"><!-- ⟩ --> </mo> </mrow> <mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="38" data-semantic-parent="65" data-semantic-operator="infixop,−"><!-- − --> </mo> <msup data-semantic-type="superscript" data-semantic-role="leftright" data-semantic-id="53" data-semantic-children="64,52" data-semantic-parent="65" data-semantic-fencepointer="51"> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="64" data-semantic-children="63" data-semantic-content="39,51" data-semantic-parent="53"> <mo fence="false" stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="39" data-semantic-parent="64"><!-- ⟨ --> </mo> <mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="63" data-semantic-children="42,60,50" data-semantic-content="61,62" data-semantic-parent="64"> <msub data-semantic-type="subscript" data-semantic-role="greekletter" data-semantic-id="42" data-semantic-children="40,41" data-semantic-parent="63"> <mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="40" data-semantic-parent="42">ψ <!-- ψ --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="41" data-semantic-parent="42">i</mi> </mrow> </msub> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="61" data-semantic-parent="63" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <mrow data-semantic-type="fenced" data-semantic-role="neutral" data-semantic-id="60" data-semantic-children="46" data-semantic-content="43,47" data-semantic-parent="63"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="neutral" data-semantic-id="43" data-semantic-parent="60" data-semantic-operator="fenced">|</mo> </mrow> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="46" data-semantic-children="44,45" data-semantic-parent="60"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="44" data-semantic-parent="46">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="45" data-semantic-parent="46">i</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="neutral" data-semantic-id="47" data-semantic-parent="60" data-semantic-operator="fenced">|</mo> </mrow> </mrow> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="62" data-semantic-parent="63" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <msub data-semantic-type="subscript" data-semantic-role="greekletter" data-semantic-id="50" data-semantic-children="48,49" data-semantic-parent="63"> <mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="48" data-semantic-parent="50">ψ <!-- ψ --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="49" data-semantic-parent="50">i</mi> </mrow> </msub> </mrow> <mo fence="false" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="51" data-semantic-parent="64"><!-- ⟩ --> </mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="52" data-semantic-parent="53">2</mn> </mrow> </msup> </mrow> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="54" data-semantic-parent="66" data-semantic-operator="fenced">]</mo> </mrow> </mrow> </mrow> </mrow> <annotation encoding="application/x-tex">{\overline {(\Delta H)^{2}}}={\frac {1}{N}}\sum _{i=1}^{N}[\langle \psi _{i}|H_{i}^{2}|\psi _{i}\rangle -\langle \psi _{i}|H_{i}|\psi _{i}\rangle ^{2}]</annotation> </semantics> </math>