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documentation:language_reference:functions:createresonantspectra [2016/10/10 09:41] – external edit 127.0.0.1documentation:language_reference:functions:createresonantspectra [2025/11/20 03:29] (current) – external edit 127.0.0.1
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 //CreateResonantSpectra($O_1$,$O_2$,$O_3$,$O_4$,$\psi$)// calculates  //CreateResonantSpectra($O_1$,$O_2$,$O_3$,$O_4$,$\psi$)// calculates 
 \begin{equation} \begin{equation}
-\langle \psi | O_3^{\dagger} \frac{1}{(\omega_1 - \mathrm{i} \Gamma_1/2 + E_0 - O_1^{\dagger})} O_4^{\dagger} \frac{1}{(\omega_2 + \mathrm{i} \Gamma_2/2 + E_0 - O_2)} O_4\frac{1}{(\omega_1 + \mathrm{i} \Gamma_1/2 + E_0 - O_1)} O_3 | \psi \rangle,+\langle \psi | O_3^{\dagger} \frac{1}{(\omega_1 - \mathrm{i} \Gamma_1/2 + E_0^{(1)} - O_1^{\dagger})} O_4^{\dagger} \frac{1}{(\omega_2 + \mathrm{i} \Gamma_2/2 + E_0^{(2)} - O_2)} O_4\frac{1}{(\omega_1 + \mathrm{i} \Gamma_1/2 + E_0^{(1)} - O_1)} O_3 | \psi \rangle,
 \end{equation} \end{equation}
-with $E_0 = \langle \psi | O_1 | \psi \rangle$. The spectrum is returned as a spectrum object. +with $E_0^{(i)} = \langle \psi | O_i | \psi \rangle$. The spectrum is returned as a spectrum object. 
 ### ###
  
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   * $\psi$ : Wavefunction   * $\psi$ : Wavefunction
   * Possible options are:   * Possible options are:
-    * "NTri1" Positive integer specifying the number of states in the Krylov basis of $O_1$. (Standard value 200) +    * "NTri1" Positive integer specifying the number of states in the Krylov basis of $O_1$. (Standard value 100) 
-    * "NTri2" Positive integer specifying the number of states in the Krylov basis of $O_2$. (Standard value 200)+    * "NTri2" Positive integer specifying the number of states in the Krylov basis of $O_2$. (Standard value 100)
     * "epsilon" Positive real defining the smallest absolute value considered different than zero. (Standard value 1.49E-8)     * "epsilon" Positive real defining the smallest absolute value considered different than zero. (Standard value 1.49E-8)
     * "restrictions1" A list of restrictions defining restrictions on configurations and occupations included for $O_1$ . Allows one to do restricted active space calculations. Note that the action of $O_3$ and $O_4$ are not restricted and all excitations they can make are included.     * "restrictions1" A list of restrictions defining restrictions on configurations and occupations included for $O_1$ . Allows one to do restricted active space calculations. Note that the action of $O_3$ and $O_4$ are not restricted and all excitations they can make are included.
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 ===== Output ===== ===== Output =====
  
-  * //G// : Spectrum object+  * //G// : Spectrum object. 
  
 +In the case that $O_3$ ($\{O_3^a, O_3^b\}$) , $O_4$ ($\{O_4^{\alpha}, O_4^{\beta}, O_4^{\gamma}\}$) and $\psi$ ($\{\psi_1,\psi_2,\psi_3\}$) are given as tables the order of spectra returned is:
 +
 +$\{$
 +$I_1^{a,\alpha}(E_0)$, $I_1^{a,\alpha}(E_1)$, $\dots$, $I_1^{a,\alpha}(E_{N_E})$,
 +$I_1^{a,\beta}(E_0)$,  $I_1^{a,\beta}(E_1)$,  $\dots$, $I_1^{a,\beta}(E_{N_E})$,
 +$I_1^{a,\gamma}(E_0)$, $I_1^{a,\gamma}(E_1)$, $\dots$, $I_1^{a,\gamma}(E_{N_E})$,
 +     
 +$I_1^{b,\alpha}(E_0)$, $I_1^{b,\alpha}(E_1)$, $\dots$, $I_1^{b,\alpha}(E_{N_E})$,
 +$I_1^{b,\beta}(E_0)$,  $I_1^{b,\beta}(E_1)$,  $\dots$, $I_1^{b,\beta}(E_{N_E})$,
 +$I_1^{b,\gamma}(E_0)$, $I_1^{b,\gamma}(E_1)$, $\dots$, $I_1^{b,\gamma}(E_{N_E})$,
 +     
 +     
 +$I_2^{a,\alpha}(E_0)$, $I_2^{a,\alpha}(E_1)$, $\dots$, $I_2^{a,\alpha}(E_{N_E})$,
 +$I_2^{a,\beta}(E_0)$,  $I_2^{a,\beta}(E_1)$,  $\dots$, $I_2^{a,\beta}(E_{N_E})$,
 +$I_2^{a,\gamma}(E_0)$, $I_2^{a,\gamma}(E_1)$, $\dots$, $I_2^{a,\gamma}(E_{N_E})$,
 +     
 +$I_2^{b,\alpha}(E_0)$, $I_2^{b,\alpha}(E_1)$, $\dots$, $I_2^{b,\alpha}(E_{N_E})$,
 +$I_2^{b,\beta}(E_0)$,  $I_2^{b,\beta}(E_1)$,  $\dots$, $I_2^{b,\beta}(E_{N_E})$,
 +$I_2^{b,\gamma}(E_0)$, $I_2^{b,\gamma}(E_1)$, $\dots$, $I_2^{b,\gamma}(E_{N_E})$,
 +     
 +     
 +$I_3^{a,\alpha}(E_0)$, $I_3^{a,\alpha}(E_1)$, $\dots$, $I_3^{a,\alpha}(E_{N_E})$,
 +$I_3^{a,\beta}(E_0)$,  $I_3^{a,\beta}(E_1)$,  $\dots$, $I_3^{a,\beta}(E_{N_E})$,
 +$I_3^{a,\gamma}(E_0)$, $I_3^{a,\gamma}(E_1)$, $\dots$, $I_3^{a,\gamma}(E_{N_E})$,
 +     
 +$I_3^{b,\alpha}(E_0)$, $I_3^{b,\alpha}(E_1)$, $\dots$, $I_3^{b,\alpha}(E_{N_E})$,
 +$I_3^{b,\beta}(E_0)$,  $I_3^{b,\beta}(E_1)$,  $\dots$, $I_3^{b,\beta}(E_{N_E})$,
 +$I_3^{b,\gamma}(E_0)$, $I_3^{b,\gamma}(E_1)$, $\dots$, $I_3^{b,\gamma}(E_{N_E})$ $\}$
 +
 +where the alphabetic, greek and numeral indices refer to $O_3$, $O_4$ and $\psi$.
 ===== Example ===== ===== Example =====
  
 ### ###
-description text+Calculates the resonant spectra for some toy Hamiltonian and transition operators.
 ### ###
  

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