Zur Navigation springen Zur Suche springen

General

Display information for equation id:math.2250.10 on revision:2250

* Page found: Dynamik des statistischen Operators (eq math.2250.10)

(force rerendering)

Occurrences on the following pages:

Hash: d5c830aa58a7bca6ed2173fef9904708

TeX (original user input):

\begin{align}
  & {{p}_{n}}=\operatorname{Tr}\left( \rho \left| n \right\rangle \left\langle  n \right| \right) \\
 & =\sum\limits_{j}{\left\langle  j \right|\sum\limits_{i}{{{w}_{i}}\left| {{\Psi }_{i}} \right\rangle \left\langle  {{\Psi }_{i}} \right|}\left| n \right\rangle \left\langle  n  |  j \right\rangle } \\
 & =\sum\limits_{j}{\underbrace{\left\langle  j  |  j \right\rangle }_{1}\sum\limits_{i}{\left\langle  {{\Psi }_{i}}  |  n \right\rangle }\left\langle  n \right|{{w}_{i}}\left| {{\Psi }_{i}} \right\rangle } \\
 & =\sum\limits_{i}{{{w}_{i}}\left\langle  n  |  {{\Psi }_{i}} \right\rangle \left\langle  {{\Psi }_{i}}  |  n \right\rangle }=\left\langle  n \right|\rho \left| n \right\rangle  
\end{align}

TeX (checked):

{\begin{aligned}&{{p}_{n}}=\operatorname {Tr} \left(\rho \left|n\right\rangle \left\langle n\right|\right)\\&=\sum \limits _{j}{\left\langle j\right|\sum \limits _{i}{{{w}_{i}}\left|{{\Psi }_{i}}\right\rangle \left\langle {{\Psi }_{i}}\right|}\left|n\right\rangle \left\langle n|j\right\rangle }\\&=\sum \limits _{j}{\underbrace {\left\langle j|j\right\rangle } _{1}\sum \limits _{i}{\left\langle {{\Psi }_{i}}|n\right\rangle }\left\langle n\right|{{w}_{i}}\left|{{\Psi }_{i}}\right\rangle }\\&=\sum \limits _{i}{{{w}_{i}}\left\langle n|{{\Psi }_{i}}\right\rangle \left\langle {{\Psi }_{i}}|n\right\rangle }=\left\langle n\right|\rho \left|n\right\rangle \end{aligned}}

LaTeXML (experimentell; verwendet MathML) rendering

MathML (34.39 KB / 3.805 KB) :

p n = Tr ( ρ | n n | ) = j j | i w i | Ψ i Ψ i | | n n | j = j j | j 1 i Ψ i | n n | w i | Ψ i = i w i n | Ψ i Ψ i | n = n | ρ | n missing-subexpression subscript 𝑝 𝑛 Tr 𝜌 ket 𝑛 bra 𝑛 missing-subexpression absent subscript 𝑗 quantum-operator-product 𝑗 subscript 𝑖 subscript 𝑤 𝑖 subscript Ψ 𝑖 bra subscript Ψ 𝑖 ket 𝑛 inner-product 𝑛 𝑗 missing-subexpression absent subscript 𝑗 subscript inner-product 𝑗 𝑗 1 subscript 𝑖 inner-product subscript Ψ 𝑖 𝑛 quantum-operator-product 𝑛 subscript 𝑤 𝑖 subscript Ψ 𝑖 missing-subexpression absent subscript 𝑖 subscript 𝑤 𝑖 inner-product 𝑛 subscript Ψ 𝑖 inner-product subscript Ψ 𝑖 𝑛 quantum-operator-product 𝑛 𝜌 𝑛 {\displaystyle{\displaystyle\begin{aligned} &\displaystyle{{p}_{n}}=% \operatorname{Tr}\left(\rho\left|n\right\rangle\left\langle n\right|\right)\\ &\displaystyle=\sum\limits_{j}{\left\langle j\right|\sum\limits_{i}{{{w}_{i}}% \left|{{\Psi}_{i}}\right\rangle\left\langle{{\Psi}_{i}}\right|}\left|n\right% \rangle\left\langle n|j\right\rangle}\\ &\displaystyle=\sum\limits_{j}{\underbrace{\left\langle j|j\right\rangle}_{1}% \sum\limits_{i}{\left\langle{{\Psi}_{i}}|n\right\rangle}\left\langle n\right|{% {w}_{i}}\left|{{\Psi}_{i}}\right\rangle}\\ &\displaystyle=\sum\limits_{i}{{{w}_{i}}\left\langle n|{{\Psi}_{i}}\right% \rangle\left\langle{{\Psi}_{i}}|n\right\rangle}=\left\langle n\right|\rho\left% |n\right\rangle\end{aligned}}}

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


MathML (experimentell; keine Bilder) rendering

MathML (4.37 KB / 535 B) :

pn=Tr(ρ|nn|)=jj|iwi|ΨiΨi||nn|j=jj|j1iΨi|nn|wi|Ψi=iwin|ΨiΨi|n=n|ρ|n

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 Dynamik des statistischen Operators page

Identifiers

  • pn
  • ρ
  • n
  • n
  • j
  • j
  • i
  • wi
  • Ψi
  • Ψi
  • n
  • n
  • j
  • j
  • j
  • j
  • i
  • Ψi
  • n
  • n
  • wi
  • Ψi
  • i
  • wi
  • n
  • Ψi
  • Ψi
  • n
  • n
  • ρ
  • n

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results