  The exact analytic solutions of the energy eigenvalue equation of the system
consisting of a free electron and one mode of the quantized radiation field are
used for studying the physical meaning of a class of number-phase minimum
uncertainty states. The states of the mode which minimize the uncertainty
product of the photon number and the Susskind and Glogower (1964) cosine
operator have been obtained by Jackiw (1968). However, these states have so far
been remained mere mathematical constructions without any physical
significance. It is proved that the most fundamental interaction in quantum
electrodynamics - namely the interaction of a free electron with a mode of the
quantized radiation field - leads quite naturally to the generation of the
mentioned minimum uncertainty states. It is shown that from the entangled
photon-electron states developing from a highly excited number state, due to
the interaction with a Gaussian electronic wave packet, the minimum uncertainty
states of Jackiw's type can be constructed. In the electron's coordinate
representation the physical meaning of the expansion coefficients of these
states are the joint probability amplitudes of simultaneous detection of an
electron and of a definite number of photons. The joint occupation
probabilities in these states preserve their functional form as time elapses,
but they vary from point to point in space-time, depending on the location of
the detected electron. An analysis of the entanglement entropies derived from
the photon number distribution and from the electron's density operator is
given.
