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Display information for equation id:math.1704.34 on revision:1704

* Page found: Zustände mit Bahn- und Spinvariablen (eq math.1704.34)

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TeX (original user input): 

\begin{align}
& \left( \begin{matrix}

{{{\hat{H}}}_{\acute{\ }B}}+\hbar {{\omega }_{l}} & 0 \\
0 & {{{\hat{H}}}_{\acute{\ }B}}-\hbar {{\omega }_{l}} \\
\end{matrix} \right)\left( \begin{matrix}

{{\left| {{\Psi }_{1}} \right\rangle }_{t}} \\

{{\left| {{\Psi }_{2}} \right\rangle }_{t}} \\
\end{matrix} \right)=i\hbar \frac{\partial }{\partial t}\left( \begin{matrix}

{{\left| {{\Psi }_{1}} \right\rangle }_{t}} \\

{{\left| {{\Psi }_{2}} \right\rangle }_{t}} \\
\end{matrix} \right) \\
& \Leftrightarrow \left( {{{\hat{H}}}_{\acute{\ }B}}+\hbar {{\omega }_{l}} \right){{\left| {{\Psi }_{1}} \right\rangle }_{t}}=i\hbar \frac{\partial }{\partial t}{{\left| {{\Psi }_{1}} \right\rangle }_{t}} \\
& \left( {{{\hat{H}}}_{\acute{\ }B}}-\hbar {{\omega }_{l}} \right){{\left| {{\Psi }_{2}} \right\rangle }_{t}}=i\hbar \frac{\partial }{\partial t}{{\left| {{\Psi }_{2}} \right\rangle }_{t}} \\
\end{align}

TeX (checked): 

{\begin{aligned}&\left({\begin{matrix}{{\hat {H}}_{{\acute {\ }}B}}+\hbar {{\omega }_{l}}&0\\0&{{\hat {H}}_{{\acute {\ }}B}}-\hbar {{\omega }_{l}}\\\end{matrix}}\right)\left({\begin{matrix}{{\left|{{\Psi }_{1}}\right\rangle }_{t}}\\{{\left|{{\Psi }_{2}}\right\rangle }_{t}}\\\end{matrix}}\right)=i\hbar {\frac {\partial }{\partial t}}\left({\begin{matrix}{{\left|{{\Psi }_{1}}\right\rangle }_{t}}\\{{\left|{{\Psi }_{2}}\right\rangle }_{t}}\\\end{matrix}}\right)\\&\Leftrightarrow \left({{\hat {H}}_{{\acute {\ }}B}}+\hbar {{\omega }_{l}}\right){{\left|{{\Psi }_{1}}\right\rangle }_{t}}=i\hbar {\frac {\partial }{\partial t}}{{\left|{{\Psi }_{1}}\right\rangle }_{t}}\\&\left({{\hat {H}}_{{\acute {\ }}B}}-\hbar {{\omega }_{l}}\right){{\left|{{\Psi }_{2}}\right\rangle }_{t}}=i\hbar {\frac {\partial }{\partial t}}{{\left|{{\Psi }_{2}}\right\rangle }_{t}}\\\end{aligned}}

LaTeXML (experimentell; verwendet MathML) rendering

MathML (52.024 KB / 5.139 KB) :

( H ^ ´ ⁢ B + ℏ ⁢ ω l 0 0 H ^ ´ ⁢ B - ℏ ⁢ ω l ) ⁢ ( | Ψ 1 ⟩ t | Ψ 2 ⟩ t ) = i ⁢ ℏ ⁢ ∂ ∂ ⁡ t ⁢ ( | Ψ 1 ⟩ t | Ψ 2 ⟩ t ) ⇔ ( H ^ ´ ⁢ B + ℏ ⁢ ω l ) ⁢ | Ψ 1 ⟩ t = i ⁢ ℏ ⁢ ∂ ∂ ⁡ t ⁢ | Ψ 1 ⟩ t ( H ^ ´ ⁢ B - ℏ ⁢ ω l ) ⁢ | Ψ 2 ⟩ t = i ⁢ ℏ ⁢ ∂ ∂ ⁡ t ⁢ | Ψ 2 ⟩ t missing-subexpression subscript ^ 𝐻 ´ absent 𝐵 Planck-constant-over-2-pi subscript 𝜔 𝑙 0 0 subscript ^ 𝐻 ´ absent 𝐵 Planck-constant-over-2-pi subscript 𝜔 𝑙 subscript ket subscript Ψ 1 𝑡 subscript ket subscript Ψ 2 𝑡 𝑖 Planck-constant-over-2-pi 𝑡 subscript ket subscript Ψ 1 𝑡 subscript ket subscript Ψ 2 𝑡 missing-subexpression ⇔ absent subscript ^ 𝐻 ´ absent 𝐵 Planck-constant-over-2-pi subscript 𝜔 𝑙 subscript ket subscript Ψ 1 𝑡 𝑖 Planck-constant-over-2-pi 𝑡 subscript ket subscript Ψ 1 𝑡 missing-subexpression subscript ^ 𝐻 ´ absent 𝐵 Planck-constant-over-2-pi subscript 𝜔 𝑙 subscript ket subscript Ψ 2 𝑡 𝑖 Planck-constant-over-2-pi 𝑡 subscript ket subscript Ψ 2 𝑡 {\displaystyle{\displaystyle\begin{aligned} &\displaystyle\left(\begin{matrix}% \par{{{\hat{H}}}_{\acute{\ }B}}+\hbar{{\omega}_{l}}&0\\ 0&{{{\hat{H}}}_{\acute{\ }B}}-\hbar{{\omega}_{l}}\\ \end{matrix}\right)\left(\begin{matrix}\par{{\left|{{\Psi}_{1}}\right\rangle}_% {t}}\\ \par{{\left|{{\Psi}_{2}}\right\rangle}_{t}}\\ \end{matrix}\right)=i\hbar\frac{\partial}{\partial t}\left(\begin{matrix}\par{% {\left|{{\Psi}_{1}}\right\rangle}_{t}}\\ \par{{\left|{{\Psi}_{2}}\right\rangle}_{t}}\\ \end{matrix}\right)\\ &\displaystyle\Leftrightarrow\left({{{\hat{H}}}_{\acute{\ }B}}+\hbar{{\omega}_% {l}}\right){{\left|{{\Psi}_{1}}\right\rangle}_{t}}=i\hbar\frac{\partial}{% \partial t}{{\left|{{\Psi}_{1}}\right\rangle}_{t}}\\ &\displaystyle\left({{{\hat{H}}}_{\acute{\ }B}}-\hbar{{\omega}_{l}}\right){{% \left|{{\Psi}_{2}}\right\rangle}_{t}}=i\hbar\frac{\partial}{\partial t}{{\left% |{{\Psi}_{2}}\right\rangle}_{t}}\\ \end{aligned}}}

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MathML (6.404 KB / 603 B) :

(H^´B+ℏωl00H^´B−ℏωl)(|Ψ1⟩t|Ψ2⟩t)=iℏ∂∂t(|Ψ1⟩t|Ψ2⟩t)⇔(H^´B+ℏωl)|Ψ1⟩t=iℏ∂∂t|Ψ1⟩t(H^´B−ℏωl)|Ψ2⟩t=iℏ∂∂t|Ψ2⟩t

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Calculated based on the variables occurring on the entire Zustände mit Bahn- und Spinvariablen page

Identifiers

  • H^
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  • B
  • ωl
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  • B
  • ωl
  • Ψ1t
  • Ψ2t
  • i
  • t
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  • H^
  • ´
  • B
  • ωl
  • Ψ1t
  • i
  • t
  • Ψ1t
  • H^
  • ´
  • B
  • ωl
  • Ψ2t
  • i
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  • Ψ2t

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