Results for: NTCIR11-Math-9

Returned 97 matches (100 formulae, 55 docs)
Lookup 10.853 ms, Re-ranking 8206.518 ms
Found 58577 tuple postings, 33632 formulae, 8479 documents

[ formulas ]

[ documents ]

[ documents-by-formula ]

0.9733
-19.0000
31.0000

{\displaystyle|{\Psi}\rangle=\sum_{{i_{1},i_{2},\alpha_{1},\alpha_{2}}}\Gamma_% {{\alpha_{1}}}^{{[1]i_{1}}}\lambda_{{\alpha_{1}}}^{{[1]}}\Gamma_{{\alpha_{1}% \alpha_{2}}}^{{[2]i_{2}}}\lambda_{{{\alpha}_{2}}}^{{[2]}}|{i_{1}i_{2}}\rangle|% {\Phi_{{\alpha_{2}}}^{{[3..N]}}}\rangle}

0.6392
-78.0000
20.0000

c_{{i_{1}i_{2}..i_{N}}}=\sum\limits_{{\alpha_{1},..,\alpha_{{N-% 1}}=0}}^{{\chi}}\Gamma_{{\alpha_{1}}}^{{[1]i_{1}}}\lambda_{{\alpha_{1}}}^{{[1]% }}\Gamma_{{\alpha_{1}\alpha_{2}}}^{{[2]i_{2}}}\lambda_{{\alpha_{2}}}^{{[2]}}% \Gamma_{{\alpha_{2}\alpha_{3}}}^{{[3]i_{3}}}\lambda_{{\alpha_{3}}}^{{[3]}}% \cdot..\cdot\Gamma_{{\alpha_{{N-2}}\alpha_{{N-1}}}}^{{[{N-1}]i_{{N-1}}}}% \lambda_{{\alpha_{{N-1}}}}^{{[N-1]}}\Gamma_{{\alpha_{{N-1}}}}^{{[N]i_{N}}}

0.6125
-103.0000
19.0000

{\displaystyle|\Psi\rangle=\sum\limits_{{i_{1},..,i_{N}=1}}^{{M}}\sum\limits_{% {\alpha_{1},..,\alpha_{{N-1}}=0}}^{{\chi}}\Gamma_{{\alpha_{1}}}^{{[1]i_{1}}}% \lambda_{{\alpha_{1}}}^{{[1]}}\Gamma_{{\alpha_{1}\alpha_{2}}}^{{[2]i_{2}}}% \lambda_{{\alpha_{2}}}^{{[2]}}\Gamma_{{\alpha_{2}\alpha_{3}}}^{{[3]i_{3}}}% \lambda_{{\alpha_{3}}}^{{[3]}}\cdot..\cdot\Gamma_{{\alpha_{{N-2}}\alpha_{{N-1}% }}}^{{[{N-1}]i_{{N-1}}}}\lambda_{{\alpha_{{N-1}}}}^{{[N-1]}}\Gamma_{{\alpha_{{% N-1}}}}^{{[N]i_{N}}}|{i_{1},i_{2},..,i_{{N-1}},i_{N}}\rangle}

0.4638
-20.0000
16.0000

{\displaystyle|{\Psi}\rangle=\sum\limits_{{i_{1},{\alpha_{1}=1}}}^{{M,\chi}}% \Gamma_{{\alpha_{1}}}^{{[1]i_{1}}}\lambda_{{\alpha_{1}}}^{{[1]}}|{i_{1}}% \rangle|{\Phi_{{\alpha_{1}}}^{{[2..N]}}}\rangle}

0.4207
-34.0000
12.0000

{\displaystyle|{\psi}\rangle=\sum\limits_{{\alpha,\beta,\gamma=1}}^{{\chi}}% \sum\limits_{{i,j=1}}^{{M}}\lambda_{{\alpha}}^{{[C-1]}}\Gamma_{{\alpha\beta}}^% {{[C]i}}\lambda_{{\beta}}^{{[C]}}\Gamma_{{\beta\gamma}}^{{[D]j}}\lambda_{{% \gamma}}^{{[D]}}|{{\alpha}ij{\gamma}}\rangle}

0.4207
-38.0000
14.0000

{\displaystyle|{\Phi_{{\alpha_{k}}}^{{[1..k]}}}\rangle=\sum_{{\alpha_{1},% \alpha_{2}..\alpha_{{k-1}}}}\Gamma_{{\alpha_{1}}}^{{[1]i_{1}}}\lambda_{{\alpha% _{1}}}^{{[1]}}\cdot\cdot\Gamma_{{\alpha_{{k-1}}\alpha_{k}}}^{{[k]i_{k}}}|{i_{1% }i_{2}..i_{k}}\rangle}

0.4100
-19.0000
10.0000

{\displaystyle|\tau_{{\alpha_{1}i_{2}}}^{{[3..N]}}\rangle=\sum_{{\alpha_{2}}}% \Gamma_{{\alpha_{1}\alpha_{2}}}^{{[2]i_{2}}}\lambda_{{{\alpha}_{2}}}^{{[2]}}|{% \Phi_{{\alpha_{2}}}^{{[3..N]}}}\rangle}

0.3485
-18.0000
10.0000

{\displaystyle|{\psi^{\prime}}\rangle=\sum\limits_{{\alpha,\gamma=1}}^{{\chi}}% \sum\limits_{{i,j=1}}^{{M}}\lambda_{{\alpha}}\Theta_{{\alpha\gamma}}^{{ij}}% \lambda_{{\gamma}}|{{\alpha}ij\gamma}\rangle}

0.3063
-14.0000
9.0000

{\displaystyle|{\Phi^{{{}^{\prime}[{{JC}}]}}}\rangle=\sum_{{i,\alpha}}\Gamma_{% {\alpha\beta}}^{{{}^{\prime}[{{C}}]i}}\lambda_{{\alpha}}|{{\alpha}i}\rangle.}

0.3063
-14.0000
7.0000

{\displaystyle|{\Phi^{{{}^{\prime}[{{DK}}]}}}\rangle=\sum_{{j,\gamma}}\Gamma_{% {\beta\gamma}}^{{{}^{\prime}[{{D}}]j}}\lambda_{{\gamma}}|{j\gamma}\rangle.}

0.2843
-17.0000
9.0000

{\displaystyle|{\Psi}\rangle=\sum_{{\alpha_{k}}}\lambda_{{{\alpha}_{k}}}^{{[k]% }}|{\Phi_{{\alpha_{k}}}^{{[1..k]}}}\rangle|{\Phi_{{\alpha_{k}}}^{{[k+1..N]}}}\rangle}

0.2748
-70.0000
9.0000

{\displaystyle|{\Phi_{{\alpha_{k}}}^{{[k+1..N]}}}\rangle=\sum_{{\alpha_{{k+1}}% ,\alpha_{{k+2}}..\alpha_{{N}}}}\Gamma_{{\alpha_{k}\alpha_{{k+1}}}}^{{[k+1]i_{{% k+1}}}}\lambda_{{\alpha_{{k+1}}}}^{{[k+1]}}\cdot\cdot\lambda_{{\alpha_{{N-1}}}% }^{{N-1}}\Gamma_{{\alpha_{{N-1}}}}^{{[N]i_{N}}}|{i_{{k+1}}i_{{k+2}}..i_{N}}\rangle}

0.2567
-45.0000
9.0000

{\displaystyle\lambda_{{\beta}}^{{{}^{\prime}}}|{\Phi_{{\beta}}^{{{}^{\prime}[% {{JC}}]}}}\rangle=\langle{\Phi_{{\beta}}^{{{}^{\prime}[{DK}]}}}|{\psi^{\prime}% }\rangle=\sum_{{i,j,\alpha,\gamma}}(\Gamma_{{\beta\gamma}}^{{{}^{\prime}[{D}]j% }})^{{*}}\Theta_{{\alpha\gamma}}^{{ij}}(\lambda_{{\gamma}})^{2}\lambda_{{% \alpha}}|{{\alpha}i}\rangle}

0.2475
-12.0000
4.0000

{\displaystyle|n\rangle=\sum_{{k\in D}}\alpha_{{nk}}|k^{{(0)}}\rangle+\lambda|% n^{{(1)}}\rangle}

0.2374
-16.0000
8.0000

{\displaystyle|{\Phi_{{\alpha_{1}}}^{{[2..N]}}}\rangle=\sum_{{i_{2}}}|{i_{2}}% \rangle|{\tau_{{\alpha_{1}i_{2}}}^{{[3..N]}}}\rangle}

0.2261
-6.0000
4.0000

{\displaystyle{|\psi\rangle}=\sum_{{k}}c_{{k}}{{\hat{a}}_{{k}}}^{{\dagger}}|0\rangle}

0.2261
-29.0000
5.0000

{\displaystyle\Theta_{{\alpha\gamma}}^{{ij}}=\sum\limits_{{\beta=1}}^{{\chi}}% \sum\limits_{{m,n=1}}^{{M}}V_{{mn}}^{{ij}}\Gamma_{{\alpha\beta}}^{{[C]m}}% \lambda_{{\beta}}\Gamma_{{\beta\gamma}}^{{[D]n}}.}

0.2201
-5.0000
5.0000

{\displaystyle|{\mathit{after}}\rangle=\sum_{i}|\epsilon_{i}\rangle\langle i|% \psi\rangle}

0.2201
-8.0000
6.0000

{\displaystyle|{\mathit{before}}\rangle=\sum_{i}|i\rangle|\epsilon\rangle% \langle i|\psi\rangle.}

0.2201
-9.0000
5.0000

{\displaystyle|{\Psi}\rangle=\sum\limits_{{i=1}}^{{M}}a_{i}|{\Phi_{i}^{A}\Phi_% {i}^{B}}\rangle}

0.2143
-29.0000
7.0000

{\displaystyle|{\psi_{{D}}^{{\bot}}}\rangle={\frac{1}{{\sqrt{\epsilon_{n}}}}}% \sum\limits_{{{{\alpha}_{n}}={\chi}_{c}}}^{{{\chi}}}\lambda_{{{\alpha}_{n}}}^{% {[n]}}|{\Phi_{{\alpha_{n}}}^{{[1..n]}}}\rangle|{\Phi_{{\alpha_{n}}}^{{[n+1..N]% }}}\rangle}

0.2143
-30.0000
7.0000

{\displaystyle|{\psi_{{D}}}\rangle={\frac{1}{{\sqrt{1-\epsilon_{n}}}}}\sum% \limits_{{{{\alpha}_{n}}=1}}^{{{\chi}_{c}}}\lambda_{{{\alpha}_{n}}}^{{[n]}}|{% \Phi_{{\alpha_{n}}}^{{[1..n]}}}\rangle|{\Phi_{{\alpha_{n}}}^{{[n+1..N]}}}\rangle}

0.2104
-5.0000
4.0000

{\displaystyle\left|\nu_{{\alpha}}\right\rangle=\sum_{{i}}U_{{\alpha i}}\left|% \nu_{{i}}\right\rangle\,}

0.2104
-22.0000
2.0000

M_{{\alpha}}=\sum_{{i_{1}<i_{2}<\cdots<i_{k}}}x_{{i_{1}}}^{{% \alpha_{1}}}x_{{i_{2}}}^{{\alpha_{2}}}\cdots x_{{i_{k}}}^{{\alpha_{k}}}.\,

0.2079
-42.0000
7.0000

{\displaystyle|{\Psi}\rangle={\frac{1}{{\sqrt{\sum\limits_{{{\alpha_{l}}=1}}^{% {{\chi}_{c}}}{|\lambda_{{{\alpha}_{l}}}^{{[l]}}|}^{2}}}}}\cdot\sum\limits_{{{{% \alpha}_{l}}=1}}^{{{\chi}_{c}}}\lambda_{{{\alpha}_{l}}}^{{[l]}}|{\Phi_{{\alpha% _{l}}}^{{[1..l]}}}\rangle|{\Phi_{{\alpha_{l}}}^{{[l+1..N]}}}\rangle,}

0.2007
-14.0000
5.0000

{\displaystyle|\Psi\rangle=\sum_{{s_{z}}}\int\limits_{R}d^{3}\,{\mathbf{r}}% \Psi({\mathbf{r}},s_{z})|{\mathbf{r}},s_{z}\rangle}

0.2007
-18.0000
6.0000

{\displaystyle|\Psi\rangle=\sum_{{\{s\}}}{\text{Tr}}[A^{{s_{1}}}A^{{s_{2}}}% \ldots A^{{s_{N}}}]|s_{1}s_{2}\ldots s_{N}\rangle}

0.1993
-17.0000
4.0000

{\displaystyle|\psi\rangle=\sum_{{s=-1,1}}a_{s}\exp\left(i\alpha_{x}-is\theta% \right)|s\rangle}

0.1925
-9.0000
6.0000

{\displaystyle|\psi\rangle=\sum_{i}{\sqrt{\lambda_{i}}}|i_{A}\rangle\otimes|i_% {B}\rangle}

0.1925
-9.0000
5.0000

{\displaystyle|\psi\rangle=\sum_{{x}}{\sqrt{p(x)}}|x_{{A}}\rangle|x_{{B}}\rangle}

0.1925
-12.0000
6.0000

{\displaystyle|\phi\rangle=\sum_{i}{\sqrt{\lambda_{i}^{\prime}}}|i_{A}^{\prime% }\rangle\otimes|i_{B}^{\prime}\rangle}

0.1832
-4.0000
4.0000

{\displaystyle\scriptstyle|\psi\rangle=\sum_{n}c_{n}|\psi_{n}\rangle}

0.1832
-7.0000
5.0000

{\displaystyle\left|\nu_{{i}}\right\rangle=\sum_{{\alpha}}U_{{\alpha i}}^{{*}}% \left|\nu_{{\alpha}}\right\rangle}

0.1832
-7.0000
4.0000

{\displaystyle|\psi\rangle=\sum_{{n=0}}^{{\infty}}a_{n}|\psi_{n}\rangle}

0.1832
-10.0000
6.0000

{\displaystyle|\psi\rangle=\sum_{{i}}{\sqrt{p_{i}}}|i\rangle\otimes|i^{\prime}% \rangle.}

0.1832
-18.0000
5.0000

{\displaystyle(AB-BA)|\Psi\rangle=\sum_{{n}}c_{n}(AB-BA)|\psi_{n}\rangle=0}

0.1832
-26.0000
1.0000

T=\sum_{{i_{1},\dots,i_{k}=1}}^{N}T_{{i_{1}i_{2}\dots i_{k}}}e^% {{i_{1}}}\otimes e^{{i_{2}}}\otimes\cdots\otimes e^{{i_{k}}}

0.1786
-12.0000
5.0000

{\displaystyle|\psi\rangle_{{AB}}=\sum_{{i,j}}c_{{ij}}|i\rangle_{A}\otimes|j% \rangle_{B}}

0.1725
-6.0000
4.0000

{\displaystyle|\psi\rangle=\sum_{{i=1}}^{N}\alpha|i\rangle}

0.1725
-9.0000
0.0000

x_{{i_{1}}}^{{\alpha_{1}}}x_{{i_{2}}}^{{\alpha_{2}}}\cdots x_{{% i_{k}}}^{{\alpha_{k}}}

0.1725
-25.0000
4.0000

{\displaystyle\Gamma_{{\alpha_{{k-1}}\alpha_{k}}}^{{{}^{\prime}[k]i_{k}}}=\sum% _{{j}}U_{{j_{k}}}^{{i_{k}}}\Gamma_{{\alpha_{{k-1}}\alpha_{k}}}^{{[k]j_{k}}}.}

0.1721
-8.0000
5.0000

{\displaystyle|{\mathit{after}}\rangle=\sum_{i}|i,\epsilon_{i}\rangle\langle i% |\psi\rangle}

0.1721
-16.0000
4.0000

{\displaystyle\rho=\sum_{{ijkl}}p_{{kl}}^{{ij}}|i\rangle\langle j|\otimes|k% \rangle\langle l|}

0.1646
-4.0000
5.0000

{\displaystyle|\Psi\rangle=\sum_{n}c_{n}|\psi_{n}\rangle}

0.1646
-4.0000
4.0000

{\displaystyle|\psi\rangle=\sum_{i}c_{i}|\phi_{i}\rangle}

{\displaystyle|\psi\rangle=\sum_{i}c_{i}|{k_{i}}\rangle}

0.1646
-5.0000
5.0000

{\displaystyle|\Psi\rangle\,=\,\sum_{i}a_{i}\,|\psi_{i}\rangle.}

0.1646
-5.0000
4.0000

{\displaystyle|\psi\rangle=\sum_{i}c_{i}|\phi_{i}\rangle.}

0.1646
-6.0000
5.0000

{\displaystyle|\psi\rangle=\sum_{i}|i\rangle\langle i|\psi\rangle}

{\displaystyle|\psi\rangle=\sum_{\nu}|\nu\rangle\langle\nu|\psi\rangle}

0.1646
-6.0000
5.0000

{\displaystyle|{\tilde{\Psi}}\rangle=\sum_{i}|{\tilde{\phi}}_{i}\rangle c_{i}}

0.1559
-2.0000
4.0000

{\displaystyle|\psi\rangle=\sum_{j}|j\rangle\,}

0.1559
-4.0000
4.0000

{\displaystyle|\psi\rangle=\sum_{m}|j,m\rangle}

0.1559
-5.0000
4.0000

{\displaystyle|A\rangle=\sum_{S}A(S)|S\rangle}

0.1559
-13.0000
5.0000

{\displaystyle\Gamma_{{\alpha_{{l-1}}\alpha_{{l}}}}^{{[l]i_{l}}},l=1,2k-1}

0.1485
-10.0000
5.0000

{\displaystyle|\psi\rangle=\sum_{{i\in{\mathbb{N}}}}\langle e_{i}|\psi\rangle|% e_{i}\rangle,}

0.1456
-1.0000
4.0000

{\displaystyle\Gamma_{{\alpha_{{0}}}}^{{[0]i_{0}}}}

0.1456
-5.0000
4.0000

{\displaystyle|\Omega\rangle=\sum_{{i=1}}^{n}|e_{i}\rangle\otimes|e_{i}\rangle}

0.1456
-8.0000
4.0000

{\displaystyle\langle\psi|\psi\rangle=\sum_{i}|c_{i}|^{2}=1.}

0.1456
-9.0000
1.0000

{\displaystyle{\hat{H}}|\Psi_{i}\rangle=\epsilon_{i}{\hat{S}}|\Psi_{i}\rangle}

0.1456
-34.0000
5.0000

{\displaystyle(c_{{\alpha_{{l-1}}\alpha_{{l}}}})^{2}=\sum\limits_{{i_{l}=1}}^{% {d}}(\Gamma_{{\alpha_{{l-1}}\alpha_{{l}}}}^{{[l]i_{l}}})^{{*}}\Gamma_{{\alpha_% {{l-1}}\alpha_{{l}}}}^{{[l]i_{l}}}}

0.1429
-6.0000
4.0000

{\displaystyle\scriptstyle|\psi\rangle_{A}=\sum_{{i}}c_{{i}}^{A}|i\rangle_{A}}

0.1429
-7.0000
4.0000

{\displaystyle\scriptstyle|\phi\rangle_{B}=\sum_{{j}}c_{{j}}^{B}|j\rangle_{B}.}

0.1429
-14.0000
3.0000

{\displaystyle|\psi\rangle_{A}|0\rangle_{B}\rightarrow\sum_{i}M_{i}|\psi% \rangle_{A}|i\rangle_{B},}

0.1363
-4.0000
4.0000

{\displaystyle|Q\rangle=\sum_{j}Q_{j}|j\rangle\,}

0.1363
-6.0000
5.0000

{\displaystyle|\Psi\rangle=a|\psi\rangle+b|\phi\rangle}

0.1363
-7.0000
2.0000

{\displaystyle\zeta_{i}(s)=\sum_{{\lambda_{j}>0}}\lambda_{j}^{{-s}}}

0.1363
-29.0000
2.0000

{\displaystyle|\Psi\rangle=\sum\limits_{{i=1}}^{{M}}c_{{i_{1}i_{2}..i_{N}}}|{i% _{1},i_{2},..,i_{{N-1}},i_{N}}\rangle}

0.1283
-4.0000
1.0000

{\displaystyle|{\Psi}\rangle=e^{{T}}|{\Phi_{0}}\rangle}

0.1283
-8.0000
1.0000

{\displaystyle{\hat{N_{i}}}|\Psi\rangle_{\nu}=N_{i}|\Psi\rangle_{\nu}}

0.1283
-9.0000
3.0000

{\displaystyle|\psi(t)\rangle=\sum_{{n}}a_{n}(t)|n\rangle}

0.1283
-9.0000
3.0000

{\displaystyle|{\Phi_{{\alpha_{1}}}^{{[1]}}}\rangle|{\Phi_{{\alpha_{1}}}^{{[2.% .N]}}}\rangle}

0.1283
-10.0000
3.0000

{\displaystyle|\Psi(t)\rangle=\sum_{n}C_{n}(t)|\Phi_{n}\rangle}

0.1283
-12.0000
4.0000

{\displaystyle|\Psi(0)\rangle=\sum_{\alpha=1}^{D}c_{\alpha}|E_{\alpha}\rangle,}

0.1187
-1.0000
4.0000

{\displaystyle|i\rangle|\epsilon\rangle}

0.1187
-6.0000
2.0000

{\displaystyle\lambda_{{\beta}}^{{{}^{\prime}}}|{\Phi_{{\beta}}^{{{}^{\prime}[% {{\it{{JC}}}}]}}}\rangle}

0.1187
-16.0000
0.0000

H=\sum_{{i_{1}}}\sum_{{i_{2}}}...\sum_{{i_{n}}}G_{{i_{1},i_{2}.% ..i_{n}}}

0.1187
-26.0000
1.0000

P=\sum_{{i_{n}=S_{n},..i_{2}=S_{2},i_{1}=S_{1}}}K_{{i_{1}i_{2}.% .i_{n}}}

0.1187
-26.0000
1.0000

P=\sum_{{i_{1}=S_{1},i_{2}=S_{2},..i_{n}=S_{n}}}K_{{i_{1}i_{2}.% .i_{n}}}

0.1171
-16.0000
2.0000

{\displaystyle\||\Psi\rangle_{\nu}\|_{\nu}^{2}=\sum_{{n=1}}^{\infty}\langle% \Psi_{n}|\Psi_{n}\rangle_{\nu}<\infty}

0.1126
-7.0000
5.0000

{\displaystyle|\psi_{\beta}\rangle=\sum_{\alpha}|\psi_{\alpha}\rangle C_{{% \alpha\beta}}}

0.1126
-7.0000
2.0000

{\displaystyle\rho=\sum_{i}\lambda_{i}|\varphi_{i}\rangle\langle\varphi_{i}|}

0.1126
-8.0000
1.0000

{\displaystyle\rho=\sum_{i}w_{i}|\alpha_{i}\rangle\langle\alpha_{i}|,}

0.1071
-3.0000
4.0000

{\displaystyle|{\text{RVB}}\rangle=\sum_{C}|C\rangle}

0.1071
-5.0000
4.0000

{\displaystyle|\psi\rangle=\sum_{i}|i\rangle\psi_{i}}

0.1071
-9.0000
4.0000

{\displaystyle|\psi\rangle=\alpha_{0}|0\rangle+\alpha_{1}|1\rangle}

{\displaystyle|\psi\rangle=\alpha_{0}|+\rangle+\alpha_{1}|-\rangle}

0.1071
-9.0000
2.0000

i\hbar{\frac{\partial}{\partial t}}|\Psi\rangle=E_{{\Psi}}|\Psi\rangle

0.1071
-9.0000
2.0000

i\hbar{\frac{d}{dt}}|\Psi\rangle={\hat{H}}|\Psi\rangle

0.1003
-6.0000
4.0000

{\displaystyle{\hat{H}}|\Psi\rangle=E_{{\Psi}}|\Psi\rangle}

0.1003
-6.0000
4.0000

H|\Psi_{{E}}\rangle=E|\Psi_{{E}}\rangle

0.1003
-8.0000
4.0000

{\displaystyle|{\Psi_{0}}\rangle=(1+C)|{\Phi_{0}}\rangle}

0.1003
-10.0000
4.0000

{\displaystyle(\sigma_{1}\otimes I)|\Psi^{+}\rangle=|\Phi^{+}\rangle.}

0.1003
-10.0000
3.0000

{\displaystyle{\mathbf{F}}_{{\alpha}}|j\rangle=\lambda_{{\alpha}}|j\rangle,% \quad\forall\alpha.}

0.0916
-5.0000
4.0000

{\displaystyle|\Psi\rangle={\mathcal{T}}|{\tilde{\Psi}}\rangle}

0.0916
-5.0000
4.0000

H|{\Psi}\rangle=E|{\Psi}\rangle

0.0916
-9.0000
4.0000

{\displaystyle|\Psi\rangle=|\psi\rangle_{{1}}\otimes|\psi\rangle_{{2}}\otimes% \ldots\otimes|\psi\rangle_{{n}}}

0.0916
-10.0000
1.0000

{\displaystyle~{}|\psi_{{\text{field}}}(0)\rangle=\sum_{n}{C_{n}|n\rangle}~{}}

0.0805
-7.0000
3.0000

L|e_{i}\rangle=\lambda_{i}|e_{i}\rangle\,;

0.0766
-13.0000
2.0000

P=\sum_{{ij}}|i\rangle\langle j|\otimes|j\rangle\langle i|