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The model is named after the Dutch physicist Hendrik Antoon Lorentz. It is a classical, phenomenological model for materials with characteristic resonance frequencies (or other characteristic energy scales) for optical absorption, e.g. ionic and molecular vibrations, interband transitions (semiconductors), phonons, and collective excitations ...
Lorentz was one of few scientists who supported Einstein's search for general relativity from the beginning – he wrote several research papers and discussed with Einstein personally and by letter. [24] For instance, he attempted to combine Einstein's formalism with Hamilton's principle (1915), [25] and to reformulate it in a coordinate-free ...
The Tauc–Lorentz model is a mathematical formula for the frequency dependence of the complex-valued relative permittivity, sometimes referred to as the dielectric function. The model has been used to fit the complex refractive index of amorphous semiconductor materials at frequencies greater than their optical band gap .
Lorentz transformations can be parametrized by rapidity φ for a boost in the direction of a three-dimensional unit vector ^ = (,,), and a rotation angle θ about a three-dimensional unit vector ^ = (,,) defining an axis, so ^ = (,,) and ^ = (,,) are together six parameters of the Lorentz group (three for rotations and three for boosts). The ...
The usual derivation is to insert a complete set of single-particle momentum states between the fields with Lorentz covariant normalization, and then to show that the Θ functions providing the causal time ordering may be obtained by a contour integral along the energy axis, if the integrand is as above (hence the infinitesimal imaginary part ...
For the standard light cone gauge the Lorentz generators M μν are cubic in terms of oscillator variables a i, and their quantization acquires well known anomaly. Consider a set b i = (M μν ,ξ i ) which contains the Lorentz group generators and internal variables ξ i , complementing M μν to the full phase space.
Rayleigh–Lorentz pendulum (or Lorentz pendulum) is a simple pendulum, but subjected to a slowly varying frequency due to an external action (frequency is varied by varying the pendulum length), named after Lord Rayleigh and Hendrik Lorentz. [1] This problem formed the basis for the concept of adiabatic invariants in mechanics. On account of ...
Keep in mind that for the classical case, there was a continuous energy spectrum that the atomic oscillator could occupy, while for the quantum case (as we've assumed) there are only two possible (eigen)states of the problem. These equations can also be stated in matrix form: