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.

Example.Quanty

-- 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 standard operators we describe several possible transition operators related to real experimental situations.

1. Basis
2. Operators
3. Wave functions
4. Expectation values
5. Eigen states
6. Spectra
7. Resonant spectra
8. Fluorescence yield