Speculation on Quantum Bound States and Radiating Charges

 The classical Maxwell equations may be used to describe charges which radiate photons if the source (say a point charged particle) accelerates. This process of radiation has even been applied even to quantum systems. For example, some argue that a quantum accelerating charge may absorb the photons it radiates. In (1), a phenomenological Hamiltonian is established to describe a diatomic molecule which is driven by a laser and behaves as an oscillator radiating in a manner linked to Larmor radiation.

    In (2), it is argued that Maxwell’s equations for a photon (no sources) represent a quantum mechanical equation similar to Dirac’s equation. If this is the case, one may argue that Maxwell’s equations with sources present should also represent quantum equations, yet classical values are used for the velocity and acceleration of a point charge. 

    In previous notes, we have described a quantum bound state in a statistical manner as a momentum distribution of free particle states exp(ipx) i.e. W(x)=wavefunction = Sum over p a(p)exp(ipx). For the case of a potential, we argue acceleration is caused by stochastic hits V(x)=Sum over k Vk exp(ikx) which change the momentum distribution form point to point. The stochastic hits may knock the particle to the right or left at any time, so it seems there is no notion of overall forward or backwards motion for any prolonged period of time as there is in classical physics. When a particle is in a state exp(ipx), it has constant velocity and is not radiating. Potential knocks occur in the forward and backward direction with equal probability if a(p)=a(-p). If Maxwell’s equations use average values such as v(x) and acceleration which do not really apply to quantum mechanics (except in an rms manner for a bound state), then one may argue that a source term j=qv(x)  is zero if “v(x)’ is in both the forward or backward direction. Even for a quantum particle moving in one direction, exp(ipx) seems to indicate constant velocity on average i.e. there may be zitterbewegung or some other type of periodic physical motion, but there is no radiation. Thus, we argue that the classical Maxwell’s equations may not really be applied to a bound quantum state if there is no distinct forward or backwards motion. It is still possible that the potential knocks could lead to radiation emission, but experimentally bound states are stable or quasi-stable, so radiation emission from the system does not occur except in the case that a photon is emitted when an excited state drops to a lower one. In such a case, it appears that a resonance decouples into two quantum resonances, one being the photon and the other being the lower energy state.