Einstein Coefficients: Spontaneous vs Stimulated Emission

This simulator models a real ensemble of two-level atoms sitting in a thermal photon bath, driven by the same A and B Einstein coefficients that make Planck's law self-consistent. Each atom independently absorbs, spontaneously emits or stimulated-emits according to the local mean photon occupation number n̄(f,T), rendered live as a cloud of instanced 3D spheres that flip colour on every transition and fire a small photon flash outward. Turn up the temperature and the excited-state population climbs but always stays a minority — turn on the external pump instead and watch the ensemble cross the population-inversion threshold that every real laser depends on.