Single-electron Schrödinger equation for many-electron systems

Second harmonic in FELs: Generation, amplification and suppression

“…1). Estimates from [28,29] of Geloni et al (9) reasonably agree with the experiment. Calibrated formulae (5),( 6) reproduce all measured harmonic powers (red solid line for n = 1, dot-dashed orange line for n = 2 and dashed green line for n = 3) and saturated power oscillations.…”

“…In waveguide FEL schemes, differently from single pass FELs, which we consider, it is possible to excite transverse modes with a complex structure, and there is no actual division into even and odd harmonics. Relevant studies were done, for example, in [9][10][11][12]. Analytical description of the harmonic generation and evolution in a single pass FEL with account for angular effects was proposed in [5,6], developing first models in [13,14], where the angular effects were ignored.…”

Visualizing the molecular wave function in σ-coordinated complexes

“…For an N-electron system, the wave function. normalΨfalse(x1false)=ρe(x1)N can be shown to satisfy an exact one-electron Schrödinger equation, describing the motion of the single electron, x 1 , in the average field of the remaining N-1 electrons, and for a specific nuclear configuration, R (Born-Oppenheimer approximation) [12-14].…”

“…As noted in reference [14] <E N−1 > represents the energy of the core after the “sudden” removal of the one electron. Thus, as previously noted, the quantity ( E N − < E N −1 >) is essentially the ionization potential as defined in Koopmans’ theorem.…”

Exchange-Correlation Potential in the Density Functional Method

“…The difference T −T s [ρ] is the so-called correlative kinetic energy [5], which, according to (4), must contribute to v xc (r), and this is precisely taken into account by the first term in (42). What has been said clearly shows that no such term can appear in the case of a system of interacting electrons.…”