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High harmonic generation strongly depends on the driving laser field and as a result the harmonics have similar temporal and spatial coherence properties. [10] High harmonics are often generated with pulse durations shorter than that of the driving laser. [11] This is due to the nonlinearity of the generation process, phase matching and ...
Symplectic integrators are designed for the numerical solution of Hamilton's equations, which read ˙ = ˙ =, where denotes the position coordinates, the momentum coordinates, and is the Hamiltonian. The set of position and momentum coordinates ( q , p ) {\displaystyle (q,p)} are called canonical coordinates .
The corresponding Schrödinger equation is easily solved, it factorizes into 3N − 6 equations for one-dimensional harmonic oscillators. The main effort in this approximate solution of the nuclear motion Schrödinger equation is the computation of the Hessian F of V and its diagonalization.
In Wilson's GF method it is assumed that the molecular kinetic energy consists only of harmonic vibrations of the atoms, i.e., overall rotational and translational energy is ignored. Normal coordinates appear also in a quantum mechanical description of the vibrational motions of the molecule and the Coriolis coupling between rotations and ...
In vibrational spectroscopy, an overtone band is the spectral band that occurs in a vibrational spectrum of a molecule when the molecule makes a transition from the ground state (v=0) to the second excited state (v=2), where v is the vibrational quantum number (a non-negative integer) obtained from solving the Schrödinger equation for the molecule.
N-th harmonic generation. Harmonic generation (HG, also called multiple harmonic generation) is a nonlinear optical process in which photons with the same frequency interact with a nonlinear material, are "combined", and generate a new photon with times the energy of the initial photons (equivalently, times the frequency and the wavelength divided by ).
The Morse potential, named after physicist Philip M. Morse, is a convenient interatomic interaction model for the potential energy of a diatomic molecule.It is a better approximation for the vibrational structure of the molecule than the quantum harmonic oscillator because it explicitly includes the effects of bond breaking, such as the existence of unbound states.
Second-harmonic generation was first demonstrated by Peter Franken, A. E. Hill, C. W. Peters, and G. Weinreich at the University of Michigan, Ann Arbor, in 1961. [9] The demonstration was made possible by the invention of the laser, which created the required high-intensity coherent light. They focused a ruby laser with a wavelength of 694 nm ...