I&#x27;m a physicist, but in a different field, but my (possibly incorrect) impression is what a quantized particle <i>is</i> is a bit mysterious when the field is strong, for example, with lensing.<p>Best example: the Hydrogen atom is supposedly quantum, but if it is quantum, where are the photons? the q^2&#x2F;r potential is a <i>mean</i> field that one finds from classical electrodynamics, it isn&#x27;t formed by the summation of photons. [Another mental poker, photons are momentum eigenstates, so how can potential be described in position space? You&#x27;d need to sum up an infinite number of them! (For EM students, recall how to represent 1&#x2F;r in spherical harmonics or in terms of sines and cosines)]<p>What happens, as I understand it, is with strong fields, one tends to use a semi-classical description because in the strong field limit, one deals with many photons, which should approach the classical limit.<p>Basically, quanta are like &quot;pertubations&quot; of the fields from their &quot;free&quot; solutions, as they are in GR (linearization of the GR field eqns) and as they are in EM. Free essentially means in the absence of sources, like charges, or masses for GR. So trying to explain general phenomena in terms of &quot;pertubations&quot;, which are basically the solutions for &quot;free&quot; fields, is not always fair.<p>One doesn&#x27;t always face this in high energy physics because in HEP, most of the incoming and outgoing states in a problem are these &quot;free&quot; solutions. For example when doing <i>scattering</i> off a hydrogen atom, the incoming states are &quot;free&quot; (a free nuclei, a free electron), so one can use photons for that phenomena, and one finds that the scattering is like scattering against a (mean) 1&#x2F;r potential.<p>But in the case where the strong fields don&#x27;t turn off, like when you are bound to a Hydrogen atom, or when considering nucleons in nuclei in the low energy limit, one turns away from the pertubative, photon&#x2F;gluon model and either solving the problem numerically or treats the fields as semi-classical, as with the Hydrogen atom. For my field of laser-plasma physics, this shows up in the so-called &quot;Volker-state&quot;, rather than treating the strong laser field as a sum of innumerable (ie., not-simulatable) photons, one treats the Laser field as a semi-classical background for the quantum guys (electrons, ions).<p>I think lensing is like strong static fields in EM. One wouldn&#x27;t really think of them in terms of quanta of the field.