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| documentation:language_reference:functions:createspectra [2017/03/01 14:40] – Maurits W. Haverkort | documentation:language_reference:functions:createspectra [2024/01/12 10:56] (current) – Maurits W. Haverkort |
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| \langle \psi | O_2^{\dagger} \frac{1}{(\omega + \mathrm{i} \Gamma/2 + E_0 - O_1)} O_2 | \psi \rangle, | \langle \psi | O_2^{\dagger} \frac{1}{(\omega + \mathrm{i} \Gamma/2 + E_0 - O_1)} O_2 | \psi \rangle, |
| \end{equation} | \end{equation} |
| with $E_0 = \langle \psi | O_1 | \psi \rangle$ and returns the result as a spectrum object and as a tri-diagonal matrix. $O_1$ and $O_2$ are allowed to be tables of operators or tables of wavefunctions. CreateSpectra can take a forth element specifying options. | with $E_0 = \langle \psi | O_1 | \psi \rangle$ and returns the result as a spectrum object and as a tri-diagonal matrix. $O_1$ and $O_2$ are allowed to be tables of operators or tables of wavefunctions. CreateSpectra can take a fourth element specifying options. |
| ### | ### |
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| * $O_1$ : Operator | * $O_1$ : Operator |
| * $O_2$ : Operator | * $O_2$ : Operator or a list of operators |
| * $\psi$ : Wavefunction | * $\psi$ : Wavefunction or a list of Wavefunctions |
| * Possible options are: | * Possible options are: |
| * "NTri" Positive integer specifying the number of states in the Krylov basis. (Standard value 200) | * "NTri" Positive integer specifying the number of states in the Krylov basis. (Default value 200) |
| * "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. (Default value 1.49E-8) |
| * "restrictions" A list of restrictions defining restrictions on configurations and occupations included. Allows one to do restricted active space calculations | * "restrictions" A list of restrictions defining restrictions on configurations and occupations included. Allows one to do restricted active space calculations |
| * "Emin" Real value defining the minimum energy in the spectra (Standard value determined such that the spectrum fits into the range | * "Emin" Real value defining the minimum energy in the spectra (Default value determined such that the spectrum fits into the range |
| * "Emax" Real value defining the maximum energy in the spectra (Standard value determined such that the spectrum fits into the range | * "Emax" Real value defining the maximum energy in the spectra (Default value determined such that the spectrum fits into the range |
| * "NE" Positive integer defining the number of points in the spectrum. (Standard value 1000) | * "NE" Positive integer defining the number of points in the spectrum. (Default value 1000) |
| * "Gamma" Positive real defining the full width half maximum Lorenzian broadening. (Standard value 10*(Emax-Emin)/NE) | * "Gamma" Positive real defining the full width half maximum Lorenzian broadening. (Default value 10*(Emax-Emin)/NE) |
| * "Tensor" Bolean defining if off diagonal elements are calculated or not. (Standard false) | * "Tensor" Bolean defining if off diagonal elements are calculated or not. (Default false) |
| | * "E0" Overwrites the standard value of $E_0 = \langle \psi | O_1 | \psi \rangle$ to the value set in the options |
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| ===== Output ===== | ===== Output ===== |
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| * //G// : Spectrum object | * //G// : Spectrum object. In the case that both a list of operators $\{O_2^a,O_2^b\}$ as well as a list of Wavefunctions $\{\psi_1,\psi_2,\psi_3\}$ is given the output order first the Wavefunctions and then the operators, i.e. $\{I_1^a,I_2^a,I_3^a,I_1^b,I_2^b,I_3^b\}$ with $a$ and $b$ referring to the index of the operators and $1,2,3$ to the index of the Wavefunctions. |
| * //T// : List representing a tri-diagonal matrix, whose resolvent is the spectral function | * //T// : List representing a tri-diagonal matrix, whose resolvent is the spectral function |
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