Jump to navigation Jump to search

General

Display information for equation id:math.1742.8 on revision:1742

* Page found: Zeitunabhängige Störungsrechnung ohne Entartung (eq math.1742.8)

(force rerendering)

Occurrences on the following pages:

Hash: b38e4ea6e96897219af61c7ba896c878

TeX (original user input): 

\left( {{{\hat{H}}}_{0}}+\varepsilon \hat{V} \right)\left( \left| {{\Psi }_{k}}^{(0)} \right\rangle +\varepsilon \left| {{\Psi }_{k}}^{(1)} \right\rangle +{{\varepsilon }^{2}}\left| {{\Psi }_{k}}^{(2)} \right\rangle +.. \right)=\left( {{E}_{k}}^{(0)}+\varepsilon {{E}_{k}}^{(1)}+{{\varepsilon }^{2}}{{E}_{k}}^{(2)}+.. \right)\left( \left| {{\Psi }_{k}}^{(0)} \right\rangle +\varepsilon \left| {{\Psi }_{k}}^{(1)} \right\rangle +.. \right)

TeX (checked): 

\left({{\hat {H}}_{0}}+\varepsilon {\hat {V}}\right)\left(\left|{{\Psi }_{k}}^{(0)}\right\rangle +\varepsilon \left|{{\Psi }_{k}}^{(1)}\right\rangle +{{\varepsilon }^{2}}\left|{{\Psi }_{k}}^{(2)}\right\rangle +..\right)=\left({{E}_{k}}^{(0)}+\varepsilon {{E}_{k}}^{(1)}+{{\varepsilon }^{2}}{{E}_{k}}^{(2)}+..\right)\left(\left|{{\Psi }_{k}}^{(0)}\right\rangle +\varepsilon \left|{{\Psi }_{k}}^{(1)}\right\rangle +..\right)

LaTeXML (experimental; uses MathML) rendering

MathML (21.621 KB / 2.795 KB) :

( H ^ 0 + ε V ^ ) ( | Ψ k ( 0 ) ⟩ + ε | Ψ k ( 1 ) ⟩ + ε 2 | Ψ k ( 2 ) ⟩ + . . ) = ( E k ( 0 ) + ε E k ( 1 ) + ε 2 E k ( 2 ) + . . ) ( | Ψ k ( 0 ) ⟩ + ε | Ψ k ( 1 ) ⟩ + . . ) fragments fragments fragments fragments fragments fragments ( subscript ^ 𝐻 0 ε ^ 𝑉 ) fragments ( | superscript subscript Ψ 𝑘 0 ⟩ ε | superscript subscript Ψ 𝑘 1 ⟩ superscript 𝜀 2 | superscript subscript Ψ 𝑘 2 ⟩ . . ) fragments ( superscript subscript 𝐸 𝑘 0 ε superscript subscript 𝐸 𝑘 1 superscript 𝜀 2 superscript subscript 𝐸 𝑘 2 . . ) fragments ( | superscript subscript Ψ 𝑘 0 ⟩ ε | superscript subscript Ψ 𝑘 1 ⟩ . . ) {\displaystyle{\displaystyle\left({{{\hat{H}}}_{0}}+\varepsilon\hat{V}\right)% \left(\left|{{\Psi}_{k}}^{(0)}\right\rangle+\varepsilon\left|{{\Psi}_{k}}^{(1)% }\right\rangle+{{\varepsilon}^{2}}\left|{{\Psi}_{k}}^{(2)}\right\rangle+..% \right)=\left({{E}_{k}}^{(0)}+\varepsilon{{E}_{k}}^{(1)}+{{\varepsilon}^{2}}{{% E}_{k}}^{(2)}+..\right)\left(\left|{{\Psi}_{k}}^{(0)}\right\rangle+\varepsilon% \left|{{\Psi}_{k}}^{(1)}\right\rangle+..\right)}} 
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle\left({{{\hat{H}}}_{0}}+\varepsilon\hat{V}\right)%&#10;\left(\left|{{\Psi}_{k}}^{(0)}\right\rangle+\varepsilon\left|{{\Psi}_{k}}^{(1)%&#10;}\right\rangle+{{\varepsilon}^{2}}\left|{{\Psi}_{k}}^{(2)}\right\rangle+..%&#10;\right)=\left({{E}_{k}}^{(0)}+\varepsilon{{E}_{k}}^{(1)}+{{\varepsilon}^{2}}{{%&#10;E}_{k}}^{(2)}+..\right)\left(\left|{{\Psi}_{k}}^{(0)}\right\rangle+\varepsilon%&#10;\left|{{\Psi}_{k}}^{(1)}\right\rangle+..\right)}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1b">
      <mrow id="p1.1.m1.1.27" xref="p1.1.m1.1.27.cmml">
        <mrow id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">
          <mrow id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">
            <mrow id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">
              <mrow id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">
                <mo id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">(</mo>
                <msub id="p1.1.m1.1.70" xref="p1.1.m1.1.70.cmml">
                  <mover accent="true" id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">
                    <mi id="p1.1.m1.1.2.2" xref="p1.1.m1.1.2.2.cmml">H</mi>
                    <mo stretchy="false" id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">^</mo>
                  </mover>
                  <mn id="p1.1.m1.1.3.1" xref="p1.1.m1.1.3.1.cmml">0</mn>
                </msub>
                <mo id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">+</mo>
                <mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">ε</mi>
                <mover accent="true" id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">
                  <mi id="p1.1.m1.1.6.2" xref="p1.1.m1.1.6.2.cmml">V</mi>
                  <mo stretchy="false" id="p1.1.m1.1.6.1" xref="p1.1.m1.1.6.1.cmml">^</mo>
                </mover>
                <mo id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">)</mo>
              </mrow>
              <mrow id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">
                <mo id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">(</mo>
                <mo id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">|</mo>
                <mmultiscripts id="p1.1.m1.1.71" xref="p1.1.m1.1.71.cmml">
                  <mi mathvariant="normal" id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">Ψ</mi>
                  <mi id="p1.1.m1.1.11.1" xref="p1.1.m1.1.11.1.cmml">k</mi>
                  <none id="p1.1.m1.1.71a" xref="p1.1.m1.1.71.cmml"/>
                  <none id="p1.1.m1.1.71b" xref="p1.1.m1.1.71.cmml"/>
                  <mrow id="p1.1.m1.1.12.1" xref="p1.1.m1.1.71.cmml">
                    <mo stretchy="false" id="p1.1.m1.1.12.1.1" xref="p1.1.m1.1.71.cmml">(</mo>
                    <mn id="p1.1.m1.1.12.1.2" xref="p1.1.m1.1.12.1.2.cmml">0</mn>
                    <mo stretchy="false" id="p1.1.m1.1.12.1.3" xref="p1.1.m1.1.71.cmml">)</mo>
                  </mrow>
                </mmultiscripts>
                <mo id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">⟩</mo>
              </mrow>
              <mo id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">+</mo>
              <mi id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">ε</mi>
              <mo id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">|</mo>
              <mmultiscripts id="p1.1.m1.1.72" xref="p1.1.m1.1.72.cmml">
                <mi mathvariant="normal" id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">Ψ</mi>
                <mi id="p1.1.m1.1.18.1" xref="p1.1.m1.1.18.1.cmml">k</mi>
                <none id="p1.1.m1.1.72a" xref="p1.1.m1.1.72.cmml"/>
                <none id="p1.1.m1.1.72b" xref="p1.1.m1.1.72.cmml"/>
                <mrow id="p1.1.m1.1.19.1" xref="p1.1.m1.1.72.cmml">
                  <mo stretchy="false" id="p1.1.m1.1.19.1.1" xref="p1.1.m1.1.72.cmml">(</mo>
                  <mn id="p1.1.m1.1.19.1.2" xref="p1.1.m1.1.19.1.2.cmml">1</mn>
                  <mo stretchy="false" id="p1.1.m1.1.19.1.3" xref="p1.1.m1.1.72.cmml">)</mo>
                </mrow>
              </mmultiscripts>
              <mo id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">⟩</mo>
            </mrow>
            <mo id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">+</mo>
            <msup id="p1.1.m1.1.73" xref="p1.1.m1.1.73.cmml">
              <mi id="p1.1.m1.1.22" xref="p1.1.m1.1.22.cmml">ε</mi>
              <mn id="p1.1.m1.1.23.1" xref="p1.1.m1.1.23.1.cmml">2</mn>
            </msup>
            <mo id="p1.1.m1.1.24" xref="p1.1.m1.1.24.cmml">|</mo>
            <mmultiscripts id="p1.1.m1.1.74" xref="p1.1.m1.1.74.cmml">
              <mi mathvariant="normal" id="p1.1.m1.1.25" xref="p1.1.m1.1.25.cmml">Ψ</mi>
              <mi id="p1.1.m1.1.26.1" xref="p1.1.m1.1.26.1.cmml">k</mi>
              <none id="p1.1.m1.1.74a" xref="p1.1.m1.1.74.cmml"/>
              <none id="p1.1.m1.1.74b" xref="p1.1.m1.1.74.cmml"/>
              <mrow id="p1.1.m1.1.27.1" xref="p1.1.m1.1.74.cmml">
                <mo stretchy="false" id="p1.1.m1.1.27.1.1" xref="p1.1.m1.1.74.cmml">(</mo>
                <mn id="p1.1.m1.1.27.1.2" xref="p1.1.m1.1.27.1.2.cmml">2</mn>
                <mo stretchy="false" id="p1.1.m1.1.27.1.3" xref="p1.1.m1.1.74.cmml">)</mo>
              </mrow>
            </mmultiscripts>
            <mo id="p1.1.m1.1.28" xref="p1.1.m1.1.28.cmml">⟩</mo>
          </mrow>
          <mo id="p1.1.m1.1.29" xref="p1.1.m1.1.29.cmml">+</mo>
          <mo id="p1.1.m1.1.30" xref="p1.1.m1.1.30.cmml">.</mo>
          <mo id="p1.1.m1.1.31" xref="p1.1.m1.1.31.cmml">.</mo>
          <mo id="p1.1.m1.1.32" xref="p1.1.m1.1.32.cmml">)</mo>
        </mrow>
        <mo id="p1.1.m1.1.33" xref="p1.1.m1.1.33.cmml">=</mo>
        <mrow id="p1.1.m1.1.23" xref="p1.1.m1.1.23.cmml">
          <mo id="p1.1.m1.1.34" xref="p1.1.m1.1.34.cmml">(</mo>
          <mmultiscripts id="p1.1.m1.1.75" xref="p1.1.m1.1.75.cmml">
            <mi id="p1.1.m1.1.35" xref="p1.1.m1.1.35.cmml">E</mi>
            <mi id="p1.1.m1.1.36.1" xref="p1.1.m1.1.36.1.cmml">k</mi>
            <none id="p1.1.m1.1.75a" xref="p1.1.m1.1.75.cmml"/>
            <none id="p1.1.m1.1.75b" xref="p1.1.m1.1.75.cmml"/>
            <mrow id="p1.1.m1.1.37.1" xref="p1.1.m1.1.75.cmml">
              <mo stretchy="false" id="p1.1.m1.1.37.1.1" xref="p1.1.m1.1.75.cmml">(</mo>
              <mn id="p1.1.m1.1.37.1.2" xref="p1.1.m1.1.37.1.2.cmml">0</mn>
              <mo stretchy="false" id="p1.1.m1.1.37.1.3" xref="p1.1.m1.1.75.cmml">)</mo>
            </mrow>
          </mmultiscripts>
          <mo id="p1.1.m1.1.38" xref="p1.1.m1.1.38.cmml">+</mo>
          <mi id="p1.1.m1.1.39" xref="p1.1.m1.1.39.cmml">ε</mi>
          <mmultiscripts id="p1.1.m1.1.76" xref="p1.1.m1.1.76.cmml">
            <mi id="p1.1.m1.1.40" xref="p1.1.m1.1.40.cmml">E</mi>
            <mi id="p1.1.m1.1.41.1" xref="p1.1.m1.1.41.1.cmml">k</mi>
            <none id="p1.1.m1.1.76a" xref="p1.1.m1.1.76.cmml"/>
            <none id="p1.1.m1.1.76b" xref="p1.1.m1.1.76.cmml"/>
            <mrow id="p1.1.m1.1.42.1" xref="p1.1.m1.1.76.cmml">
              <mo stretchy="false" id="p1.1.m1.1.42.1.1" xref="p1.1.m1.1.76.cmml">(</mo>
              <mn id="p1.1.m1.1.42.1.2" xref="p1.1.m1.1.42.1.2.cmml">1</mn>
              <mo stretchy="false" id="p1.1.m1.1.42.1.3" xref="p1.1.m1.1.76.cmml">)</mo>
            </mrow>
          </mmultiscripts>
          <mo id="p1.1.m1.1.43" xref="p1.1.m1.1.43.cmml">+</mo>
          <msup id="p1.1.m1.1.77" xref="p1.1.m1.1.77.cmml">
            <mi id="p1.1.m1.1.44" xref="p1.1.m1.1.44.cmml">ε</mi>
            <mn id="p1.1.m1.1.45.1" xref="p1.1.m1.1.45.1.cmml">2</mn>
          </msup>
          <mmultiscripts id="p1.1.m1.1.78" xref="p1.1.m1.1.78.cmml">
            <mi id="p1.1.m1.1.46" xref="p1.1.m1.1.46.cmml">E</mi>
            <mi id="p1.1.m1.1.47.1" xref="p1.1.m1.1.47.1.cmml">k</mi>
            <none id="p1.1.m1.1.78a" xref="p1.1.m1.1.78.cmml"/>
            <none id="p1.1.m1.1.78b" xref="p1.1.m1.1.78.cmml"/>
            <mrow id="p1.1.m1.1.48.1" xref="p1.1.m1.1.78.cmml">
              <mo stretchy="false" id="p1.1.m1.1.48.1.1" xref="p1.1.m1.1.78.cmml">(</mo>
              <mn id="p1.1.m1.1.48.1.2" xref="p1.1.m1.1.48.1.2.cmml">2</mn>
              <mo stretchy="false" id="p1.1.m1.1.48.1.3" xref="p1.1.m1.1.78.cmml">)</mo>
            </mrow>
          </mmultiscripts>
          <mo id="p1.1.m1.1.49" xref="p1.1.m1.1.49.cmml">+</mo>
          <mo id="p1.1.m1.1.50" xref="p1.1.m1.1.50.cmml">.</mo>
          <mo id="p1.1.m1.1.51" xref="p1.1.m1.1.51.cmml">.</mo>
          <mo id="p1.1.m1.1.52" xref="p1.1.m1.1.52.cmml">)</mo>
        </mrow>
        <mrow id="p1.1.m1.1.26" xref="p1.1.m1.1.26.cmml">
          <mo id="p1.1.m1.1.53" xref="p1.1.m1.1.53.cmml">(</mo>
          <mo id="p1.1.m1.1.54" xref="p1.1.m1.1.54.cmml">|</mo>
          <mmultiscripts id="p1.1.m1.1.79" xref="p1.1.m1.1.79.cmml">
            <mi mathvariant="normal" id="p1.1.m1.1.55" xref="p1.1.m1.1.55.cmml">Ψ</mi>
            <mi id="p1.1.m1.1.56.1" xref="p1.1.m1.1.56.1.cmml">k</mi>
            <none id="p1.1.m1.1.79a" xref="p1.1.m1.1.79.cmml"/>
            <none id="p1.1.m1.1.79b" xref="p1.1.m1.1.79.cmml"/>
            <mrow id="p1.1.m1.1.57.1" xref="p1.1.m1.1.79.cmml">
              <mo stretchy="false" id="p1.1.m1.1.57.1.1" xref="p1.1.m1.1.79.cmml">(</mo>
              <mn id="p1.1.m1.1.57.1.2" xref="p1.1.m1.1.57.1.2.cmml">0</mn>
              <mo stretchy="false" id="p1.1.m1.1.57.1.3" xref="p1.1.m1.1.79.cmml">)</mo>
            </mrow>
          </mmultiscripts>
          <mo id="p1.1.m1.1.58" xref="p1.1.m1.1.58.cmml">⟩</mo>
        </mrow>
        <mo id="p1.1.m1.1.59" xref="p1.1.m1.1.59.cmml">+</mo>
        <mi id="p1.1.m1.1.60" xref="p1.1.m1.1.60.cmml">ε</mi>
        <mo id="p1.1.m1.1.61" xref="p1.1.m1.1.61.cmml">|</mo>
        <mmultiscripts id="p1.1.m1.1.80" xref="p1.1.m1.1.80.cmml">
          <mi mathvariant="normal" id="p1.1.m1.1.62" xref="p1.1.m1.1.62.cmml">Ψ</mi>
          <mi id="p1.1.m1.1.63.1" xref="p1.1.m1.1.63.1.cmml">k</mi>
          <none id="p1.1.m1.1.80a" xref="p1.1.m1.1.80.cmml"/>
          <none id="p1.1.m1.1.80b" xref="p1.1.m1.1.80.cmml"/>
          <mrow id="p1.1.m1.1.64.1" xref="p1.1.m1.1.80.cmml">
            <mo stretchy="false" id="p1.1.m1.1.64.1.1" xref="p1.1.m1.1.80.cmml">(</mo>
            <mn id="p1.1.m1.1.64.1.2" xref="p1.1.m1.1.64.1.2.cmml">1</mn>
            <mo stretchy="false" id="p1.1.m1.1.64.1.3" xref="p1.1.m1.1.80.cmml">)</mo>
          </mrow>
        </mmultiscripts>
        <mo id="p1.1.m1.1.65" xref="p1.1.m1.1.65.cmml">⟩</mo>
      </mrow>
      <mo id="p1.1.m1.1.66" xref="p1.1.m1.1.66.cmml">+</mo>
      <mo id="p1.1.m1.1.67" xref="p1.1.m1.1.67.cmml">.</mo>
      <mo id="p1.1.m1.1.68" xref="p1.1.m1.1.68.cmml">.</mo>
      <mo id="p1.1.m1.1.69" xref="p1.1.m1.1.69.cmml">)</mo>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1c">
      <cerror id="p1.1.m1.1d">
        <csymbol cd="ambiguous" id="p1.1.m1.1e">fragments</csymbol>
        <cerror id="p1.1.m1.1.27.cmml" xref="p1.1.m1.1.27">
          <csymbol cd="ambiguous" id="p1.1.m1.1.27a.cmml" xref="p1.1.m1.1.27">fragments</csymbol>
          <cerror id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19">
            <csymbol cd="ambiguous" id="p1.1.m1.1.19a.cmml" xref="p1.1.m1.1.19">fragments</csymbol>
            <cerror id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">
              <csymbol cd="ambiguous" id="p1.1.m1.1.18a.cmml" xref="p1.1.m1.1.18">fragments</csymbol>
              <cerror id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">
                <csymbol cd="ambiguous" id="p1.1.m1.1.12a.cmml" xref="p1.1.m1.1.12">fragments</csymbol>
                <cerror id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">
                  <csymbol cd="ambiguous" id="p1.1.m1.1.3a.cmml" xref="p1.1.m1.1.3">fragments</csymbol>
                  <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">(</ci>
                  <apply id="p1.1.m1.1.70.cmml" xref="p1.1.m1.1.70">
                    <csymbol cd="ambiguous" id="p1.1.m1.1.70.1.cmml" xref="p1.1.m1.1.70">subscript</csymbol>
                    <apply id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">
                      <ci id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">^</ci>
                      <ci id="p1.1.m1.1.2.2.cmml" xref="p1.1.m1.1.2.2">𝐻</ci>
                    </apply>
                    <cn type="integer" id="p1.1.m1.1.3.1.cmml" xref="p1.1.m1.1.3.1">0</cn>
                  </apply>
                  <plus id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4"/>
                  <csymbol cd="unknown" id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">ε</csymbol>
                  <apply id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">
                    <ci id="p1.1.m1.1.6.1.cmml" xref="p1.1.m1.1.6.1">^</ci>
                    <ci id="p1.1.m1.1.6.2.cmml" xref="p1.1.m1.1.6.2">𝑉</ci>
                  </apply>
                  <ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">)</ci>
                </cerror>
                <cerror id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">
                  <csymbol cd="ambiguous" id="p1.1.m1.1.11a.cmml" xref="p1.1.m1.1.11">fragments</csymbol>
                  <ci id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">(</ci>
                  <ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">|</ci>
                  <apply id="p1.1.m1.1.71.cmml" xref="p1.1.m1.1.71">
                    <csymbol cd="ambiguous" id="p1.1.m1.1.71.1.cmml" xref="p1.1.m1.1.71">superscript</csymbol>
                    <apply id="p1.1.m1.1.71.2.cmml" xref="p1.1.m1.1.71">
                      <csymbol cd="ambiguous" id="p1.1.m1.1.71.2.1.cmml" xref="p1.1.m1.1.71">subscript</csymbol>
                      <ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">Ψ</ci>
                      <ci id="p1.1.m1.1.11.1.cmml" xref="p1.1.m1.1.11.1">𝑘</ci>
                    </apply>
                    <cn type="integer" id="p1.1.m1.1.12.1.2.cmml" xref="p1.1.m1.1.12.1.2">0</cn>
                  </apply>
                  <ci id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">⟩</ci>
                </cerror>
                <plus id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14"/>
                <csymbol cd="unknown" id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">ε</csymbol>
                <ci id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">|</ci>
                <apply id="p1.1.m1.1.72.cmml" xref="p1.1.m1.1.72">
                  <csymbol cd="ambiguous" id="p1.1.m1.1.72.1.cmml" xref="p1.1.m1.1.72">superscript</csymbol>
                  <apply id="p1.1.m1.1.72.2.cmml" xref="p1.1.m1.1.72">
                    <csymbol cd="ambiguous" id="p1.1.m1.1.72.2.1.cmml" xref="p1.1.m1.1.72">subscript</csymbol>
                    <ci id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">Ψ</ci>
                    <ci id="p1.1.m1.1.18.1.cmml" xref="p1.1.m1.1.18.1">𝑘</ci>
                  </apply>
                  <cn type="integer" id="p1.1.m1.1.19.1.2.cmml" xref="p1.1.m1.1.19.1.2">1</cn>
                </apply>
                <ci id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20">⟩</ci>
              </cerror>
              <plus id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21"/>
              <apply id="p1.1.m1.1.73.cmml" xref="p1.1.m1.1.73">
                <csymbol cd="ambiguous" id="p1.1.m1.1.73.1.cmml" xref="p1.1.m1.1.73">superscript</csymbol>
                <ci id="p1.1.m1.1.22.cmml" xref="p1.1.m1.1.22">𝜀</ci>
                <cn type="integer" id="p1.1.m1.1.23.1.cmml" xref="p1.1.m1.1.23.1">2</cn>
              </apply>
              <ci id="p1.1.m1.1.24.cmml" xref="p1.1.m1.1.24">|</ci>
              <apply id="p1.1.m1.1.74.cmml" xref="p1.1.m1.1.74">
                <csymbol cd="ambiguous" id="p1.1.m1.1.74.1.cmml" xref="p1.1.m1.1.74">superscript</csymbol>
                <apply id="p1.1.m1.1.74.2.cmml" xref="p1.1.m1.1.74">
                  <csymbol cd="ambiguous" id="p1.1.m1.1.74.2.1.cmml" xref="p1.1.m1.1.74">subscript</csymbol>
                  <ci id="p1.1.m1.1.25.cmml" xref="p1.1.m1.1.25">Ψ</ci>
                  <ci id="p1.1.m1.1.26.1.cmml" xref="p1.1.m1.1.26.1">𝑘</ci>
                </apply>
                <cn type="integer" id="p1.1.m1.1.27.1.2.cmml" xref="p1.1.m1.1.27.1.2">2</cn>
              </apply>
              <ci id="p1.1.m1.1.28.cmml" xref="p1.1.m1.1.28">⟩</ci>
            </cerror>
            <plus id="p1.1.m1.1.29.cmml" xref="p1.1.m1.1.29"/>
            <ci id="p1.1.m1.1.30.cmml" xref="p1.1.m1.1.30">.</ci>
            <ci id="p1.1.m1.1.31.cmml" xref="p1.1.m1.1.31">.</ci>
            <ci id="p1.1.m1.1.32.cmml" xref="p1.1.m1.1.32">)</ci>
          </cerror>
          <eq id="p1.1.m1.1.33.cmml" xref="p1.1.m1.1.33"/>
          <cerror id="p1.1.m1.1.23.cmml" xref="p1.1.m1.1.23">
            <csymbol cd="ambiguous" id="p1.1.m1.1.23a.cmml" xref="p1.1.m1.1.23">fragments</csymbol>
            <ci id="p1.1.m1.1.34.cmml" xref="p1.1.m1.1.34">(</ci>
            <apply id="p1.1.m1.1.75.cmml" xref="p1.1.m1.1.75">
              <csymbol cd="ambiguous" id="p1.1.m1.1.75.1.cmml" xref="p1.1.m1.1.75">superscript</csymbol>
              <apply id="p1.1.m1.1.75.2.cmml" xref="p1.1.m1.1.75">
                <csymbol cd="ambiguous" id="p1.1.m1.1.75.2.1.cmml" xref="p1.1.m1.1.75">subscript</csymbol>
                <ci id="p1.1.m1.1.35.cmml" xref="p1.1.m1.1.35">𝐸</ci>
                <ci id="p1.1.m1.1.36.1.cmml" xref="p1.1.m1.1.36.1">𝑘</ci>
              </apply>
              <cn type="integer" id="p1.1.m1.1.37.1.2.cmml" xref="p1.1.m1.1.37.1.2">0</cn>
            </apply>
            <plus id="p1.1.m1.1.38.cmml" xref="p1.1.m1.1.38"/>
            <csymbol cd="unknown" id="p1.1.m1.1.39.cmml" xref="p1.1.m1.1.39">ε</csymbol>
            <apply id="p1.1.m1.1.76.cmml" xref="p1.1.m1.1.76">
              <csymbol cd="ambiguous" id="p1.1.m1.1.76.1.cmml" xref="p1.1.m1.1.76">superscript</csymbol>
              <apply id="p1.1.m1.1.76.2.cmml" xref="p1.1.m1.1.76">
                <csymbol cd="ambiguous" id="p1.1.m1.1.76.2.1.cmml" xref="p1.1.m1.1.76">subscript</csymbol>
                <ci id="p1.1.m1.1.40.cmml" xref="p1.1.m1.1.40">𝐸</ci>
                <ci id="p1.1.m1.1.41.1.cmml" xref="p1.1.m1.1.41.1">𝑘</ci>
              </apply>
              <cn type="integer" id="p1.1.m1.1.42.1.2.cmml" xref="p1.1.m1.1.42.1.2">1</cn>
            </apply>
            <plus id="p1.1.m1.1.43.cmml" xref="p1.1.m1.1.43"/>
            <apply id="p1.1.m1.1.77.cmml" xref="p1.1.m1.1.77">
              <csymbol cd="ambiguous" id="p1.1.m1.1.77.1.cmml" xref="p1.1.m1.1.77">superscript</csymbol>
              <ci id="p1.1.m1.1.44.cmml" xref="p1.1.m1.1.44">𝜀</ci>
              <cn type="integer" id="p1.1.m1.1.45.1.cmml" xref="p1.1.m1.1.45.1">2</cn>
            </apply>
            <apply id="p1.1.m1.1.78.cmml" xref="p1.1.m1.1.78">
              <csymbol cd="ambiguous" id="p1.1.m1.1.78.1.cmml" xref="p1.1.m1.1.78">superscript</csymbol>
              <apply id="p1.1.m1.1.78.2.cmml" xref="p1.1.m1.1.78">
                <csymbol cd="ambiguous" id="p1.1.m1.1.78.2.1.cmml" xref="p1.1.m1.1.78">subscript</csymbol>
                <ci id="p1.1.m1.1.46.cmml" xref="p1.1.m1.1.46">𝐸</ci>
                <ci id="p1.1.m1.1.47.1.cmml" xref="p1.1.m1.1.47.1">𝑘</ci>
              </apply>
              <cn type="integer" id="p1.1.m1.1.48.1.2.cmml" xref="p1.1.m1.1.48.1.2">2</cn>
            </apply>
            <plus id="p1.1.m1.1.49.cmml" xref="p1.1.m1.1.49"/>
            <ci id="p1.1.m1.1.50.cmml" xref="p1.1.m1.1.50">.</ci>
            <ci id="p1.1.m1.1.51.cmml" xref="p1.1.m1.1.51">.</ci>
            <ci id="p1.1.m1.1.52.cmml" xref="p1.1.m1.1.52">)</ci>
          </cerror>
          <cerror id="p1.1.m1.1.26.cmml" xref="p1.1.m1.1.26">
            <csymbol cd="ambiguous" id="p1.1.m1.1.26a.cmml" xref="p1.1.m1.1.26">fragments</csymbol>
            <ci id="p1.1.m1.1.53.cmml" xref="p1.1.m1.1.53">(</ci>
            <ci id="p1.1.m1.1.54.cmml" xref="p1.1.m1.1.54">|</ci>
            <apply id="p1.1.m1.1.79.cmml" xref="p1.1.m1.1.79">
              <csymbol cd="ambiguous" id="p1.1.m1.1.79.1.cmml" xref="p1.1.m1.1.79">superscript</csymbol>
              <apply id="p1.1.m1.1.79.2.cmml" xref="p1.1.m1.1.79">
                <csymbol cd="ambiguous" id="p1.1.m1.1.79.2.1.cmml" xref="p1.1.m1.1.79">subscript</csymbol>
                <ci id="p1.1.m1.1.55.cmml" xref="p1.1.m1.1.55">Ψ</ci>
                <ci id="p1.1.m1.1.56.1.cmml" xref="p1.1.m1.1.56.1">𝑘</ci>
              </apply>
              <cn type="integer" id="p1.1.m1.1.57.1.2.cmml" xref="p1.1.m1.1.57.1.2">0</cn>
            </apply>
            <ci id="p1.1.m1.1.58.cmml" xref="p1.1.m1.1.58">⟩</ci>
          </cerror>
          <plus id="p1.1.m1.1.59.cmml" xref="p1.1.m1.1.59"/>
          <csymbol cd="unknown" id="p1.1.m1.1.60.cmml" xref="p1.1.m1.1.60">ε</csymbol>
          <ci id="p1.1.m1.1.61.cmml" xref="p1.1.m1.1.61">|</ci>
          <apply id="p1.1.m1.1.80.cmml" xref="p1.1.m1.1.80">
            <csymbol cd="ambiguous" id="p1.1.m1.1.80.1.cmml" xref="p1.1.m1.1.80">superscript</csymbol>
            <apply id="p1.1.m1.1.80.2.cmml" xref="p1.1.m1.1.80">
              <csymbol cd="ambiguous" id="p1.1.m1.1.80.2.1.cmml" xref="p1.1.m1.1.80">subscript</csymbol>
              <ci id="p1.1.m1.1.62.cmml" xref="p1.1.m1.1.62">Ψ</ci>
              <ci id="p1.1.m1.1.63.1.cmml" xref="p1.1.m1.1.63.1">𝑘</ci>
            </apply>
            <cn type="integer" id="p1.1.m1.1.64.1.2.cmml" xref="p1.1.m1.1.64.1.2">1</cn>
          </apply>
          <ci id="p1.1.m1.1.65.cmml" xref="p1.1.m1.1.65">⟩</ci>
        </cerror>
        <plus id="p1.1.m1.1.66.cmml" xref="p1.1.m1.1.66"/>
        <ci id="p1.1.m1.1.67.cmml" xref="p1.1.m1.1.67">.</ci>
        <ci id="p1.1.m1.1.68.cmml" xref="p1.1.m1.1.68">.</ci>
        <ci id="p1.1.m1.1.69.cmml" xref="p1.1.m1.1.69">)</ci>
      </cerror>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1f">{\displaystyle{\displaystyle\left({{{\hat{H}}}_{0}}+\varepsilon\hat{V}\right)%
\left(\left|{{\Psi}_{k}}^{(0)}\right\rangle+\varepsilon\left|{{\Psi}_{k}}^{(1)%
}\right\rangle+{{\varepsilon}^{2}}\left|{{\Psi}_{k}}^{(2)}\right\rangle+..%
\right)=\left({{E}_{k}}^{(0)}+\varepsilon{{E}_{k}}^{(1)}+{{\varepsilon}^{2}}{{%
E}_{k}}^{(2)}+..\right)\left(\left|{{\Psi}_{k}}^{(0)}\right\rangle+\varepsilon%
\left|{{\Psi}_{k}}^{(1)}\right\rangle+..\right)}}</annotation>
  </semantics>
</math>

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


SVG (MathML can be enabled via browser plugin) rendering

MathML (8.565 KB / 780 B) :

( H ^ 0 + ε V ^ ) ( | Ψ k ( 0 ) ⟩ + ε | Ψ k ( 1 ) ⟩ + ε 2 | Ψ k ( 2 ) ⟩ + . . ) = ( E k ( 0 ) + ε E k ( 1 ) + ε 2 E k ( 2 ) + . . ) ( | Ψ k ( 0 ) ⟩ + ε | Ψ k ( 1 ) ⟩ + . . ) {\displaystyle \left({{\hat {H}}_{0}}+\varepsilon {\hat {V}}\right)\left(\left|{{\Psi }_{k}}^{(0)}\right\rangle +\varepsilon \left|{{\Psi }_{k}}^{(1)}\right\rangle +{{\varepsilon }^{2}}\left|{{\Psi }_{k}}^{(2)}\right\rangle +..\right)=\left({{E}_{k}}^{(0)}+\varepsilon {{E}_{k}}^{(1)}+{{\varepsilon }^{2}}{{E}_{k}}^{(2)}+..\right)\left(\left|{{\Psi }_{k}}^{(0)}\right\rangle +\varepsilon \left|{{\Psi }_{k}}^{(1)}\right\rangle +..\right)} 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \left({{\hat {H}}_{0}}+\varepsilon {\hat {V}}\right)\left(\left|{{\Psi }_{k}}^{(0)}\right\rangle +\varepsilon \left|{{\Psi }_{k}}^{(1)}\right\rangle +{{\varepsilon }^{2}}\left|{{\Psi }_{k}}^{(2)}\right\rangle +..\right)=\left({{E}_{k}}^{(0)}+\varepsilon {{E}_{k}}^{(1)}+{{\varepsilon }^{2}}{{E}_{k}}^{(2)}+..\right)\left(\left|{{\Psi }_{k}}^{(0)}\right\rangle +\varepsilon \left|{{\Psi }_{k}}^{(1)}\right\rangle +..\right)}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mrow>
          <mo>(</mo>
          <mrow>
            <mrow class="MJX-TeXAtom-ORD">
              <msub>
                <mrow class="MJX-TeXAtom-ORD">
                  <mrow class="MJX-TeXAtom-ORD">
                    <mover>
                      <mi>H</mi>
                      <mo stretchy="false">&#x005E;<!-- ^ --></mo>
                    </mover>
                  </mrow>
                </mrow>
                <mrow class="MJX-TeXAtom-ORD">
                  <mn>0</mn>
                </mrow>
              </msub>
            </mrow>
            <mo>+</mo>
            <mi>&#x03B5;<!-- ε --></mi>
            <mrow class="MJX-TeXAtom-ORD">
              <mrow class="MJX-TeXAtom-ORD">
                <mover>
                  <mi>V</mi>
                  <mo stretchy="false">&#x005E;<!-- ^ --></mo>
                </mover>
              </mrow>
            </mrow>
          </mrow>
          <mo>)</mo>
        </mrow>
        <mrow>
          <mo>(</mo>
          <mrow>
            <mrow>
              <mo>|</mo>
              <msup>
                <mrow class="MJX-TeXAtom-ORD">
                  <msub>
                    <mrow class="MJX-TeXAtom-ORD">
                      <mi mathvariant="normal">&#x03A8;<!-- Ψ --></mi>
                    </mrow>
                    <mrow class="MJX-TeXAtom-ORD">
                      <mi>k</mi>
                    </mrow>
                  </msub>
                </mrow>
                <mrow class="MJX-TeXAtom-ORD">
                  <mo stretchy="false">(</mo>
                  <mn>0</mn>
                  <mo stretchy="false">)</mo>
                </mrow>
              </msup>
              <mo>&#x27E9;</mo>
            </mrow>
            <mo>+</mo>
            <mi>&#x03B5;<!-- ε --></mi>
            <mrow>
              <mo>|</mo>
              <msup>
                <mrow class="MJX-TeXAtom-ORD">
                  <msub>
                    <mrow class="MJX-TeXAtom-ORD">
                      <mi mathvariant="normal">&#x03A8;<!-- Ψ --></mi>
                    </mrow>
                    <mrow class="MJX-TeXAtom-ORD">
                      <mi>k</mi>
                    </mrow>
                  </msub>
                </mrow>
                <mrow class="MJX-TeXAtom-ORD">
                  <mo stretchy="false">(</mo>
                  <mn>1</mn>
                  <mo stretchy="false">)</mo>
                </mrow>
              </msup>
              <mo>&#x27E9;</mo>
            </mrow>
            <mo>+</mo>
            <mrow class="MJX-TeXAtom-ORD">
              <msup>
                <mrow class="MJX-TeXAtom-ORD">
                  <mi>&#x03B5;<!-- ε --></mi>
                </mrow>
                <mrow class="MJX-TeXAtom-ORD">
                  <mn>2</mn>
                </mrow>
              </msup>
            </mrow>
            <mrow>
              <mo>|</mo>
              <msup>
                <mrow class="MJX-TeXAtom-ORD">
                  <msub>
                    <mrow class="MJX-TeXAtom-ORD">
                      <mi mathvariant="normal">&#x03A8;<!-- Ψ --></mi>
                    </mrow>
                    <mrow class="MJX-TeXAtom-ORD">
                      <mi>k</mi>
                    </mrow>
                  </msub>
                </mrow>
                <mrow class="MJX-TeXAtom-ORD">
                  <mo stretchy="false">(</mo>
                  <mn>2</mn>
                  <mo stretchy="false">)</mo>
                </mrow>
              </msup>
              <mo>&#x27E9;</mo>
            </mrow>
            <mo>+</mo>
            <mo>.</mo>
            <mo>.</mo>
          </mrow>
          <mo>)</mo>
        </mrow>
        <mo>=</mo>
        <mrow>
          <mo>(</mo>
          <mrow>
            <msup>
              <mrow class="MJX-TeXAtom-ORD">
                <msub>
                  <mrow class="MJX-TeXAtom-ORD">
                    <mi>E</mi>
                  </mrow>
                  <mrow class="MJX-TeXAtom-ORD">
                    <mi>k</mi>
                  </mrow>
                </msub>
              </mrow>
              <mrow class="MJX-TeXAtom-ORD">
                <mo stretchy="false">(</mo>
                <mn>0</mn>
                <mo stretchy="false">)</mo>
              </mrow>
            </msup>
            <mo>+</mo>
            <mi>&#x03B5;<!-- ε --></mi>
            <msup>
              <mrow class="MJX-TeXAtom-ORD">
                <msub>
                  <mrow class="MJX-TeXAtom-ORD">
                    <mi>E</mi>
                  </mrow>
                  <mrow class="MJX-TeXAtom-ORD">
                    <mi>k</mi>
                  </mrow>
                </msub>
              </mrow>
              <mrow class="MJX-TeXAtom-ORD">
                <mo stretchy="false">(</mo>
                <mn>1</mn>
                <mo stretchy="false">)</mo>
              </mrow>
            </msup>
            <mo>+</mo>
            <mrow class="MJX-TeXAtom-ORD">
              <msup>
                <mrow class="MJX-TeXAtom-ORD">
                  <mi>&#x03B5;<!-- ε --></mi>
                </mrow>
                <mrow class="MJX-TeXAtom-ORD">
                  <mn>2</mn>
                </mrow>
              </msup>
            </mrow>
            <msup>
              <mrow class="MJX-TeXAtom-ORD">
                <msub>
                  <mrow class="MJX-TeXAtom-ORD">
                    <mi>E</mi>
                  </mrow>
                  <mrow class="MJX-TeXAtom-ORD">
                    <mi>k</mi>
                  </mrow>
                </msub>
              </mrow>
              <mrow class="MJX-TeXAtom-ORD">
                <mo stretchy="false">(</mo>
                <mn>2</mn>
                <mo stretchy="false">)</mo>
              </mrow>
            </msup>
            <mo>+</mo>
            <mo>.</mo>
            <mo>.</mo>
          </mrow>
          <mo>)</mo>
        </mrow>
        <mrow>
          <mo>(</mo>
          <mrow>
            <mrow>
              <mo>|</mo>
              <msup>
                <mrow class="MJX-TeXAtom-ORD">
                  <msub>
                    <mrow class="MJX-TeXAtom-ORD">
                      <mi mathvariant="normal">&#x03A8;<!-- Ψ --></mi>
                    </mrow>
                    <mrow class="MJX-TeXAtom-ORD">
                      <mi>k</mi>
                    </mrow>
                  </msub>
                </mrow>
                <mrow class="MJX-TeXAtom-ORD">
                  <mo stretchy="false">(</mo>
                  <mn>0</mn>
                  <mo stretchy="false">)</mo>
                </mrow>
              </msup>
              <mo>&#x27E9;</mo>
            </mrow>
            <mo>+</mo>
            <mi>&#x03B5;<!-- ε --></mi>
            <mrow>
              <mo>|</mo>
              <msup>
                <mrow class="MJX-TeXAtom-ORD">
                  <msub>
                    <mrow class="MJX-TeXAtom-ORD">
                      <mi mathvariant="normal">&#x03A8;<!-- Ψ --></mi>
                    </mrow>
                    <mrow class="MJX-TeXAtom-ORD">
                      <mi>k</mi>
                    </mrow>
                  </msub>
                </mrow>
                <mrow class="MJX-TeXAtom-ORD">
                  <mo stretchy="false">(</mo>
                  <mn>1</mn>
                  <mo stretchy="false">)</mo>
                </mrow>
              </msup>
              <mo>&#x27E9;</mo>
            </mrow>
            <mo>+</mo>
            <mo>.</mo>
            <mo>.</mo>
          </mrow>
          <mo>)</mo>
        </mrow>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle \left({{\hat {H}}_{0}}+\varepsilon {\hat {V}}\right)\left(\left|{{\Psi }_{k}}^{(0)}\right\rangle +\varepsilon \left|{{\Psi }_{k}}^{(1)}\right\rangle +{{\varepsilon }^{2}}\left|{{\Psi }_{k}}^{(2)}\right\rangle +..\right)=\left({{E}_{k}}^{(0)}+\varepsilon {{E}_{k}}^{(1)}+{{\varepsilon }^{2}}{{E}_{k}}^{(2)}+..\right)\left(\left|{{\Psi }_{k}}^{(0)}\right\rangle +\varepsilon \left|{{\Psi }_{k}}^{(1)}\right\rangle +..\right)}</annotation>
  </semantics>
</math>

SVG (16.39 KB / 4.756 KB) :

{\displaystyle \left({{\hat {H}}_{0}}+\varepsilon {\hat {V}}\right)\left(\left|{{\Psi }_{k}}^{(0)}\right\rangle +\varepsilon \left|{{\Psi }_{k}}^{(1)}\right\rangle +{{\varepsilon }^{2}}\left|{{\Psi }_{k}}^{(2)}\right\rangle +..\right)=\left({{E}_{k}}^{(0)}+\varepsilon {{E}_{k}}^{(1)}+{{\varepsilon }^{2}}{{E}_{k}}^{(2)}+..\right)\left(\left|{{\Psi }_{k}}^{(0)}\right\rangle +\varepsilon \left|{{\Psi }_{k}}^{(1)}\right\rangle +..\right)}

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Similar pages

Calculated based on the variables occurring on the entire Zeitunabhängige Störungsrechnung ohne Entartung page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results

Retrieved from "http://physikerwelt.de:8080/w/index.php?title=Special:FormulaInfo"