Zelfconsistentiemethoden

Zelfconsistentiemethoden, also known as self-consistency methods, are a class of computational techniques used to solve problems where the solution depends on itself. This self-referential nature arises in various scientific and engineering disciplines. A common characteristic of self-consistency methods is an iterative approach, where an initial guess or approximation is made, and then this approximation is refined based on the problem's inherent dependencies. The process continues until the solution converges, meaning that subsequent iterations produce negligible changes.

These methods are particularly prevalent in quantum mechanics and condensed matter physics, where the behavior of many interacting particles must be determined simultaneously. For instance, the Hartree-Fock method in atomic and molecular physics uses a self-consistent field approximation. In this approach, the motion of each electron is influenced by an average field created by all other electrons, and this field is updated iteratively until it is consistent with the electron wavefunctions it generates.

Beyond physics, self-consistency plays a role in fields like economics, where market equilibrium depends on the decisions of numerous agents, and in computer science, particularly in algorithms for constraint satisfaction or belief propagation. The core idea is to iteratively adjust the components of a system until they mutually satisfy all the defined conditions and relationships, leading to a stable and consistent outcome.