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Display information for equation id:math.1632.13 on revision:1632

* Page found: Eigenwerte und Eigenzustände von hermiteschen Operatoren (eq math.1632.13)

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Eigenwerte und Eigenzustände von hermiteschen Operatoren Eq: math.1632.13

Hash: 503704582177163abf389d3d2825616c

TeX (original user input):

\begin{align}
& \left\langle  {{\Psi }_{1}} \right|\hat{F}\left| {{\Psi }_{2}} \right\rangle ={{F}_{2}}\left\langle  {{\Psi }_{1}}  |  {{\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}}  |  {{\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}}  |  {{\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}}|{{\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}}|{{\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}}|{{\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}}

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\begin{aligned} ⟨ Ψ_{1} | \hat{F} | Ψ_{2} ⟩ = F_{2} ⟨ Ψ_{1} | Ψ_{2} ⟩ \\ ⟨ Ψ_{2} | \hat{F} | Ψ_{1} ⟩ = F_{1} ⟨ Ψ_{2} | Ψ_{1} ⟩ = ⟨ Ψ_{1} | \hat{F} | Ψ_{2} ⟩ * = F_{2} ⟨ Ψ_{1} | Ψ_{2} ⟩ f a l l s \hat{F} = {\hat{F}}^{+}, F_{2} = F_{2} * \\ ⟨ Ψ_{2} | \hat{F} | Ψ_{1} ⟩ = ⟨ {\hat{F}}^{+} Ψ_{2} | Ψ_{1} ⟩ = F_{2} ⟨ Ψ_{2} | Ψ_{1} ⟩ \\ ⟨ Ψ_{2} | \hat{F} | Ψ_{1} ⟩ - ⟨ Ψ_{2} | \hat{F} | Ψ_{1} ⟩ = (F_{2} - F_{1}) ⟨ Ψ_{2} | Ψ_{1} ⟩ \end{aligned}

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Identifiers

$Ψ_{1}$

$\hat{F}$

$Ψ_{2}$

$F_{2}$

$Ψ_{1}$

$Ψ_{2}$

$Ψ_{2}$

$\hat{F}$

$Ψ_{1}$

$F_{1}$

$Ψ_{2}$

$Ψ_{1}$

$Ψ_{1}$

$\hat{F}$

$Ψ_{2}$

$F_{2}$

$Ψ_{1}$

$Ψ_{2}$

$f$

$a$

$l$

$l$

$s$

$\hat{F}$

$\hat{F}$

$F_{2}$

$F_{2}$

$Ψ_{2}$

$\hat{F}$

$Ψ_{1}$

$\hat{F}$

$Ψ_{2}$

$Ψ_{1}$

$F_{2}$

$Ψ_{2}$

$Ψ_{1}$

$Ψ_{2}$

$\hat{F}$

$Ψ_{1}$

$Ψ_{2}$

$\hat{F}$

$Ψ_{1}$

$F_{2}$

$F_{1}$

$Ψ_{2}$

$Ψ_{1}$

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