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 — documentation:basics:spectra [2016/10/10 09:40] (current) 2016/10/06 20:36 Maurits W. Haverkort created 2016/10/06 20:36 Maurits W. Haverkort created Line 1: Line 1: + {{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. + ​ + -- Creating a spectrum from a starting state psi + -- a transition operator T + -- and an Hamiltonian H + G = CreateSpectra(H,​T,​psi) + ​ + ### + + ### + 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|]]