Analyzing Photon- Electron Interaction by Quantum Matrix Approach*

For interactive photon-electron system, the linear combination of photon number states is

adopted which suitably describes absorbing and emitting photon process by an electron and the

quantum matrix method is utilized to find hamiltonian’s eigenvalue and eigenfunction. The

quantum self-field notion arises due to sufficient input energy. In this paper, “bare” electron

appears near the center of mass (positively shifted away from mass-shell status) and the

change of its energy denoted by “bare mass” m 0 is deemed minor since it absorbs and emits

virtual photons in an isotropical manner so to position itself better. The eigenvalue and

eigenfunction discovered in this analysis are similar to those in linear harmonic oscillator

formulation. The photon emission event is linked to n = 1 state with probable photon

number 1.7. Because of electron’s position, emitted photon has an isotropic angular

distribution in the C.M. frame and energy dependence for absorbing and emission

photon amplitude is 1/P 2 where P is the upper limit of virtual photon momentum with c

set to be unit. If initially electron is at rest in the laboratory frame, the amplitude in this

frame is (1 + 2q)/{1.5m[(1 + 2q) 1/2 -1](1 + q – qcosψ’)} 2 where q = p i /m with p i being

incoming photon energy and p i along z-axis. ψ’ is the angle between emitted photon

and z-axis.