Semiclassical

The semiclassical approach to the relativistic theory has been recently worked out by several authors and the #92;hbar² corrections to the earlier established TF relativistic theory have been derived¹⁷⁻¹⁹.

2020, Bei-Lok B. Hu, Enric Verdaguer, Semiclassical and Stochastic Gravity, Cambridge University Press, page 337, Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein—Langevin equation, which has in addition sources due to the noise kernel.

2024, Chaoyuan Zhu, Semiclassical Nonadiabatic Molecular Dynamics, Springer, page 109, Of course, the main problem with such semiclassical treatment is to find suitable coordinate[s] in which [a] multidimensional scattering or reaction Schrödinger equation has to be expanded into the certain one-dimensional many-state coupled Schrödinger equations like Equation 4.219.