BETAnsatz

The BETAnsatz is a numerical method used in computational physics and chemistry to solve the Bethe-Salpeter equation (BSE). The BSE is a relativistic quantum mechanical equation that describes the bound states of two interacting particles, most commonly an electron and a hole, forming an exciton. Solving the BSE exactly is computationally very expensive.

The BETAnsatz, introduced by R. R. Rzazewski and coworkers, provides an approximation to the BSE by assuming a specific form for the wave function of the electron-hole pair. This assumed form, or "ansatz," typically involves a product of single-particle wave functions, often obtained from density functional theory (DFT) calculations, and a correlation function that accounts for the interaction between the electron and the hole.

By making this ansatz, the BSE, which is an integral equation, is transformed into a set of algebraic equations. This significantly simplifies the problem and reduces the computational cost, making it feasible to study excitonic properties for larger systems or perform more extensive calculations.

The BETAnsatz is widely used for calculating optical properties, such as absorption and emission spectra, as well as exciton binding energies and wave functions. While it is an approximation and has limitations, it offers a good balance between accuracy and computational efficiency for many practical applications in condensed matter physics and quantum chemistry. Different versions of the BETAnsatz exist, varying in the specific form of the correlation function and the inclusion of relativistic effects.