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Display information for equation id:math.2446.21 on revision:2446

* Page found: Thermodynamischer Limes (eq math.2446.21)

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Thermodynamischer Limes Eq: math.2446.21

Hash: 8a6dc285ad19a327f0d43ccf2447016a

TeX (original user input):

\begin{align}

& \begin{matrix}

\lim   \\

\alpha \to \infty   \\

\end{matrix}\frac{\left\langle {{\left( \alpha \Delta {{M}^{n}} \right)}^{2}} \right\rangle }{{{\left\langle \alpha {{M}^{n}} \right\rangle }^{2}}}=-\begin{matrix}

\lim   \\

\alpha \to \infty   \\

\end{matrix}\alpha \frac{1}{{{\left\langle \alpha {{M}^{n}} \right\rangle }^{2}}}\frac{{{\partial }^{2}}\Psi \left( z \right)}{\partial {{\lambda }_{n}}^{2}} \\

& \frac{{{\partial }^{2}}\Psi \left( z \right)}{\partial {{\lambda }_{n}}^{2}}<\infty  \\

& \Rightarrow \begin{matrix}

\lim   \\

\alpha \to \infty   \\

\end{matrix}\frac{\left\langle {{\left( \alpha \Delta {{M}^{n}} \right)}^{2}} \right\rangle }{{{\left\langle \alpha {{M}^{n}} \right\rangle }^{2}}}=-\begin{matrix}

\lim   \\

\alpha \to \infty   \\

\end{matrix}\alpha \frac{1}{{{\left\langle \alpha {{M}^{n}} \right\rangle }^{2}}}\frac{{{\partial }^{2}}\Psi \left( z \right)}{\partial {{\lambda }_{n}}^{2}}=0 \\

\end{align}

TeX (checked):

{\begin{aligned}&{\begin{matrix}\lim \\\alpha \to \infty \\\end{matrix}}{\frac {\left\langle {{\left(\alpha \Delta {{M}^{n}}\right)}^{2}}\right\rangle }{{\left\langle \alpha {{M}^{n}}\right\rangle }^{2}}}=-{\begin{matrix}\lim \\\alpha \to \infty \\\end{matrix}}\alpha {\frac {1}{{\left\langle \alpha {{M}^{n}}\right\rangle }^{2}}}{\frac {{{\partial }^{2}}\Psi \left(z\right)}{\partial {{\lambda }_{n}}^{2}}}\\&{\frac {{{\partial }^{2}}\Psi \left(z\right)}{\partial {{\lambda }_{n}}^{2}}}<\infty \\&\Rightarrow {\begin{matrix}\lim \\\alpha \to \infty \\\end{matrix}}{\frac {\left\langle {{\left(\alpha \Delta {{M}^{n}}\right)}^{2}}\right\rangle }{{\left\langle \alpha {{M}^{n}}\right\rangle }^{2}}}=-{\begin{matrix}\lim \\\alpha \to \infty \\\end{matrix}}\alpha {\frac {1}{{\left\langle \alpha {{M}^{n}}\right\rangle }^{2}}}{\frac {{{\partial }^{2}}\Psi \left(z\right)}{\partial {{\lambda }_{n}}^{2}}}=0\\\end{aligned}}

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\begin{aligned} \begin{matrix} \lim \\ α \to \infty \end{matrix} \frac{⟨ {(α Δ M^{n})}^{2} ⟩}{{⟨ α M^{n} ⟩}^{2}} = - \begin{matrix} \lim \\ α \to \infty \end{matrix} α \frac{1}{{⟨ α M^{n} ⟩}^{2}} \frac{\partial^{2} Ψ (z)}{\partial {λ_{n}}^{2}} \\ \frac{\partial^{2} Ψ (z)}{\partial {λ_{n}}^{2}} < \infty \\ \Rightarrow \begin{matrix} \lim \\ α \to \infty \end{matrix} \frac{⟨ {(α Δ M^{n})}^{2} ⟩}{{⟨ α M^{n} ⟩}^{2}} = - \begin{matrix} \lim \\ α \to \infty \end{matrix} α \frac{1}{{⟨ α M^{n} ⟩}^{2}} \frac{\partial^{2} Ψ (z)}{\partial {λ_{n}}^{2}} = 0 \end{aligned}

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Identifiers

$α$

$α$

$Δ$

$M$

$n$

$α$

$M$

$n$

$α$

$α$

$α$

$M$

$n$

$Ψ$

$z$

$λ_{n}$

$Ψ$

$z$

$λ_{n}$

$α$

$α$

$Δ$

$M$

$n$

$α$

$M$

$n$

$α$

$α$

$α$

$M$

$n$

$Ψ$

$z$

$λ_{n}$

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