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====== 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|]]