Unperturbed

Unperturbed describes a system or state that is not affected by perturbations or disturbances. In science and mathematics, it serves as a baseline or reference configuration from which small external influences are analyzed. The term is frequently used to distinguish the idealized, solvable part of a problem from additional forces, interactions, or fluctuations that complicate the motion or behavior of the system.

In physics, particularly quantum mechanics and dynamical systems, the unperturbed problem is described by an unperturbed Hamiltonian or equations of motion. A perturbing term, representing a small external influence, is then added to study its effects. Time-independent perturbation theory yields corrections to energy levels and eigenstates, while time-dependent perturbation theory describes transitions and dynamics induced by the perturbation. The approach assumes the perturbation is sufficiently small that the solution can be expanded as a series around the unperturbed case.

In celestial and classical mechanics, the motion of a body under an idealized force law (such as the two-body gravitational problem) is treated as unperturbed, with deviations arising from additional bodies, non-spherical mass distributions, atmospheric drag, or other forces treated as perturbations. The concept is likewise used in other fields to indicate conditions, models, or data that have not been altered by external disturbances.

Etymology-wise, unperturbed combines the prefix un- with perturbed, which derives from Latin perturbare, meaning to disturb or disrupt. In practice, the term signals a baseline state used for theoretical approximation or comparison.