Jump to navigation Jump to search

General

Display information for equation id:math.1628.13 on revision:1628

* Page found: Eigenwerte und Eigenzustände von hermiteschen Operatoren (eq math.1628.13)

(force rerendering)

Occurrences on the following pages:

Hash: 8b131bdef59f08b8140cb6f2dad1b4a9

TeX (original user input): 

\begin{align}
& \left\langle  {{\Psi }_{1}} \right|\hat{F}\left| {{\Psi }_{2}} \right\rangle ={{F}_{2}}\left\langle  {{\Psi }_{1}} \right|\left| {{\Psi }_{2}} \right\rangle  \\
& \left\langle  {{\Psi }_{2}} \right|\hat{F}\left| {{\Psi }_{1}} \right\rangle ={{F}_{1}}\left\langle  {{\Psi }_{2}} | {{\Psi }_{1}} \right\rangle =\left\langle  {{\Psi }_{1}} \right|\hat{F}\left| {{\Psi }_{2}} \right\rangle *={{F}_{2}}\left\langle  {{\Psi }_{1}} \right|\left| {{\Psi }_{2}} \right\rangle \quad falls\ \hat{F}={{{\hat{F}}}^{+}},{{F}_{2}}={{F}_{2}}* \\
& \left\langle  {{\Psi }_{2}} \right|\hat{F}\left| {{\Psi }_{1}} \right\rangle =\left\langle  {{{\hat{F}}}^{+}}{{\Psi }_{2}} \right|\left| {{\Psi }_{1}} \right\rangle ={{F}_{2}}\left\langle  {{\Psi }_{2}} | {{\Psi }_{1}} \right\rangle  \\
& \left\langle  {{\Psi }_{2}} \right|\hat{F}\left| {{\Psi }_{1}} \right\rangle -\left\langle  {{\Psi }_{2}} \right|\hat{F}\left| {{\Psi }_{1}} \right\rangle =\left( {{F}_{2}}-{{F}_{1}} \right)\left\langle  {{\Psi }_{2}} | {{\Psi }_{1}} \right\rangle  \\ 

\end{align}

TeX (checked): 

{\begin{aligned}&\left\langle {{\Psi }_{1}}\right|{\hat {F}}\left|{{\Psi }_{2}}\right\rangle ={{F}_{2}}\left\langle {{\Psi }_{1}}\right|\left|{{\Psi }_{2}}\right\rangle \\&\left\langle {{\Psi }_{2}}\right|{\hat {F}}\left|{{\Psi }_{1}}\right\rangle ={{F}_{1}}\left\langle {{\Psi }_{2}}|{{\Psi }_{1}}\right\rangle =\left\langle {{\Psi }_{1}}\right|{\hat {F}}\left|{{\Psi }_{2}}\right\rangle *={{F}_{2}}\left\langle {{\Psi }_{1}}\right|\left|{{\Psi }_{2}}\right\rangle \quad falls\ {\hat {F}}={{\hat {F}}^{+}},{{F}_{2}}={{F}_{2}}*\\&\left\langle {{\Psi }_{2}}\right|{\hat {F}}\left|{{\Psi }_{1}}\right\rangle =\left\langle {{\hat {F}}^{+}}{{\Psi }_{2}}\right|\left|{{\Psi }_{1}}\right\rangle ={{F}_{2}}\left\langle {{\Psi }_{2}}|{{\Psi }_{1}}\right\rangle \\&\left\langle {{\Psi }_{2}}\right|{\hat {F}}\left|{{\Psi }_{1}}\right\rangle -\left\langle {{\Psi }_{2}}\right|{\hat {F}}\left|{{\Psi }_{1}}\right\rangle =\left({{F}_{2}}-{{F}_{1}}\right)\left\langle {{\Psi }_{2}}|{{\Psi }_{1}}\right\rangle \\\end{aligned}}

LaTeXML (experimental; uses MathML) rendering

MathML (0 B / 8 B) :

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


MathML (experimental; no images) rendering

MathML (6.467 KB / 522 B) :

⟨Ψ1|F̂|Ψ2⟩=F2⟨Ψ1||Ψ2⟩⟨Ψ2|F̂|Ψ1⟩=F1⟨Ψ2|Ψ1⟩=⟨Ψ1|F̂|Ψ2⟩∗=F2⟨Ψ1||Ψ2⟩falls F̂=F̂+,F2=F2∗⟨Ψ2|F̂|Ψ1⟩=⟨F̂+Ψ2||Ψ1⟩=F2⟨Ψ2|Ψ1⟩⟨Ψ2|F̂|Ψ1⟩−⟨Ψ2|F̂|Ψ1⟩=(F2−F1)⟨Ψ2|Ψ1⟩
<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mtable displaystyle="true"><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mi>Ψ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><mover><mi>F</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi>Ψ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo stretchy="false">=</mo><msub><mi>F</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mi>Ψ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi>Ψ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mi>Ψ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><mover><mi>F</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi>Ψ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo stretchy="false">=</mo><msub><mi>F</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mi>Ψ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">|</mo><msub><mi>Ψ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo stretchy="false">=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mi>Ψ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><mover><mi>F</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi>Ψ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo stretchy="false">∗</mo><mo stretchy="false">=</mo><msub><mi>F</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mi>Ψ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi>Ψ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mspace width="1em"></mspace><mi>f</mi><mi>a</mi><mi>l</mi><mi>l</mi><mi>s</mi><mtext>&#160;</mtext><mover><mi>F</mi><mo stretchy="false">̂</mo></mover><mo stretchy="false">=</mo><msup><mover><mi>F</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mo stretchy="false" lspace="0" rspace="0">+</mo></mrow></msup><mo>,</mo><msub><mi>F</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">=</mo><msub><mi>F</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">∗</mo></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mi>Ψ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><mover><mi>F</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi>Ψ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo stretchy="false">=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msup><mover><mi>F</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mo stretchy="false" lspace="0" rspace="0">+</mo></mrow></msup><msub><mi>Ψ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi>Ψ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo stretchy="false">=</mo><msub><mi>F</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mi>Ψ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">|</mo><msub><mi>Ψ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mi>Ψ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><mover><mi>F</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi>Ψ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo stretchy="false">−</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mi>Ψ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><mover><mi>F</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi>Ψ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo stretchy="false">=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>F</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">−</mo><msub><mi>F</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mi>Ψ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">|</mo><msub><mi>Ψ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>

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 Eigenwerte und Eigenzustände von hermiteschen Operatoren page

Identifiers

  • Ψ1
  • F̂
  • Ψ2
  • F2
  • Ψ1
  • Ψ2
  • Ψ2
  • F̂
  • Ψ1
  • F1
  • Ψ2
  • Ψ1
  • Ψ1
  • F̂
  • Ψ2
  • F2
  • Ψ1
  • Ψ2
  • f
  • a
  • l
  • l
  • s
  • F̂
  • F̂
  • F2
  • F2
  • Ψ2
  • F̂
  • Ψ1
  • F̂
  • Ψ2
  • Ψ1
  • F2
  • Ψ2
  • Ψ1
  • Ψ2
  • F̂
  • Ψ1
  • Ψ2
  • F̂
  • Ψ1
  • F2
  • F1
  • Ψ2
  • Ψ1

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"