quasiclassical

Quasiclassical refers to methods and concepts that bridge quantum mechanics and classical physics. In practice, it denotes approaches in which some degrees of freedom are treated classically while quantum effects are retained through phases, amplitudes or reduced descriptions. Quasiclassical descriptions are appropriate when the characteristic action is large compared with Planck's constant, so quantum wave phenomena can be approximated by locally classical trajectories with quantum corrections.

Common examples appear in quantum mechanics and wave propagation: the Wentzel–Kramers–Brillouin (WKB) approximation, the eikonal approximation, and other semiclassical methods that express wavefunctions as exp(i S/ħ) along classical paths. These techniques describe high-momentum or slowly varying potentials, scattering, tunneling and bound states. They capture phase information along trajectories and use classical dynamics to determine amplitudes, with quantum corrections added perturbatively.

In condensed matter physics, quasiclassical theory refers to a formalism for superconductivity using quasiclassical Green's functions. It reduces high-energy degrees of freedom to yield the Eilenberger equations or Usadel equations, simplifying transport and nonequilibrium phenomena in superconducting structures and heterostructures.

The term is sometimes used interchangeably with semiclassical physics, but quasiclassical emphasizes retaining coherence and phase information through a predominantly classical description rather than a full quantum treatment.

Limitations include breakdown when action is not large or near turning points; applicability requires variations on scales larger than the wavelength, and in superconductivity depends on mean free path and energy scales. It is not a universal replacement for full quantum theory.