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documentation:basics:spectra [2016/10/10 09:40] (current)
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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|]]
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