High order harmonic generation: The role of the acceleration matrix elements and of the bound and continuum transitions

The emission time of harmonics emitted by a molecule

“…Since numerical simulations require the choice of a finite integration spatial box and finite x integration step, the computer code provides only a finite number of bound levels and reproduces the free states with a discrete set of states resembling those of a particle in a box. These features are similar to those found when dealing with atoms and an extensive discussion can be found in [11] and references therein.…”

“…Of course such an effect unveils a highly nonlinear response of the atom to the driving force and cannot profitably be interpreted by means of standard perturbation theory for it would require an expansion of the atomic wavefunction in the electric field intensity at least as large as ω M /ω L [10][11][12]. A common approach to the problem consists of a numerical solution of the time-dependent Schrödinger equation with given initial condition ih ∂ψ(x, t) ∂t = { Ĥ0 + V (x, t)}ψ(x, t); ψ(x, 0) = φ(x) (1) with Ĥ0 ≡ ( p2 )/(2m) + U (x) the laser free atomic Hamiltonian, U (x) the atomic potential energy, V (x, t) the laser-atom interaction energy and, finally, φ(x) the initial condition.…”

“…A common approach to the problem consists of a numerical solution of the time-dependent Schrödinger equation with given initial condition ih ∂ψ(x, t) ∂t = { Ĥ0 + V (x, t)}ψ(x, t); ψ(x, 0) = φ(x) (1) with Ĥ0 ≡ ( p2 )/(2m) + U (x) the laser free atomic Hamiltonian, U (x) the atomic potential energy, V (x, t) the laser-atom interaction energy and, finally, φ(x) the initial condition. Here we have assumed a one-dimensional, single-electron model to describe the problem at hand; the usefulness as well as the drawbacks of these widely adopted assumptions have been extensively investigated and seem well understood so that they do not need to be discussed again here [11].…”

Constraints on the spatial variation of Planck constant

“…By a suitable choice of the free parameters, the energy gap between two bound states or the size of a real atom can be recovered. In both forms the free parameter a is of the order of the Bohr radius a 0 = 5.29 × 10 −9 cm and provides the atomic size [45,46]. In Ref.…”

The electron wavefunction in laser-assisted bremsstrahlung

“…The interested reader is referred to [12], where one can find all the information needed for the purpose. The quantum averaged acceleration to be introduced in the Larmor formula ( 4) is found by means of the Ehrenfest theorem (3).…”