Quantum Systems

A quantum system is here taken to be a collection of single-particle orbitals $\vec{P}$, arranged into multiple configurations, and a set of mixing coefficients $\vec{c}$. As an example, the helium ground state 1s² may be approximated a linear combination of Slater determinants:

\[\begin{equation} \Psi(\textrm{1s²}) \approx \sum_i c_i \Phi(\gamma_i), \end{equation}\]

where $\gamma_i$ denotes a configuration of single-electron orbitals and $c_i$ its associated mixing coefficient. A low-order approximation may be achieved with the three Slater determinants formed from the 1s and 2s orbitals:

\[\begin{equation} \Phi(\textrm{1s²}), \quad \Phi(\textrm{1s 2s}), \quad \Phi(\textrm{2s²}). \end{equation}\]

Similar ideas can be employed for molecules, etc.

diff(quantum_system[; kwargs...])

Varies the the quantum_system with respect to all orbitals. Used to derive the multi-configurational Hartree–Fock equations. To be overloaded by the implementation of AbstractQuantumSystem.