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+ | {{indexmenu_n>6}} | ||

+ | ====== Spectra ====== | ||

+ | ### | ||

+ | Spectra are implemented by calculating the Green's function. We calculate the complex energy dependent quantity: | ||

+ | $$ | ||

+ | G(\omega) = \bigg\langle \psi_i \bigg| T^{\dagger} \frac{1}{\omega - H + \imath \Gamma/2} T \bigg| \psi_i \bigg\rangle, | ||

+ | $$ | ||

+ | with $T$ and $H$ an operator given in second quantization and $\psi_i$ a many particle wavefunction. | ||

+ | <code Quanty Example.Quanty> | ||

+ | -- Creating a spectrum from a starting state psi | ||

+ | -- a transition operator T | ||

+ | -- and an Hamiltonian H | ||

+ | G = CreateSpectra(H,T,psi) | ||

+ | </code> | ||

+ | ### | ||

+ | |||

+ | ### | ||

+ | For photoemission the transition operator $T$ would be an annihilation operator, for absorption the product of a creation and annihilation operator and for inverse photoemission a creation operator. In the section on[[documentation:standard_operators:start| standard operators]] we describe several possible transition operators related to real experimental situations. | ||

+ | ### | ||

+ | |||

+ | ===== Index ===== | ||

+ | - [[documentation:basics:basis|]] | ||

+ | - [[documentation:basics:operators|]] | ||

+ | - [[documentation:basics:wave_functions|]] | ||

+ | - [[documentation:basics:expectation_values|]] | ||

+ | - [[documentation:basics:eigen_states|]] | ||

+ | - Spectra | ||

+ | - [[documentation:basics:resonant_spectra|]] | ||

+ | - [[documentation:basics:fluorescence_yield|]] |