Planck quanta

Presents the Fokker-Planck quantum description of open systems, by considering the drift and diffusion contributions in quantum evolution, as based on a non-equilibrium Lagrangian, lading with generating of the so called Markovian families of electronic localization functions, accommodating the Thom s catastrophe theory in an iimovative maimer, thus directly describing the atomic valence distribution as well as the molecular formation. 

Sound has frequencies in the range of 10-10 s , while vibrations in molecules are in the range of lO -lO s". In a crystal, the lower range of frequencies corresponds to acoustic phonons and the higher range to optical phonons. Optical phonons are similar to molecular vibrations. The smallest wavelengths have atomic or molecular dimensions. For both photons and phonons, the energy quantum is the Planck quantum, hv. 

The miderstanding of the quantum mechanics of atoms was pioneered by Bohr, in his theory of the hydrogen atom. This combined the classical ideas on planetary motion—applicable to the atom because of the fomial similarity of tlie gravitational potential to tlie Coulomb potential between an electron and nucleus—with the quantum ideas that had recently been introduced by Planck and Einstein. This led eventually to the fomial theory of quaiitum mechanics, first discovered by Heisenberg, and most conveniently expressed by Schrodinger in the wave equation that bears his name. 

In the previous section we discussed light and matter at equilibrium in a two-level quantum system. For the remainder of this section we will be interested in light and matter which are not at equilibrium. In particular, laser light is completely different from the thennal radiation described at the end of the previous section. In the first place, only one, or a small number of states of the field are occupied, in contrast with the Planck distribution of occupation numbers in thennal radiation. Second, the field state can have a precise phase-, in thennal radiation this phase is assumed to be random. If multiple field states are occupied in a laser they can have a precise phase relationship, something which is achieved in lasers by a teclmique called mode-locking Multiple frequencies with a precise phase relation give rise to laser pulses in time. Nanosecond experiments... 

Here h(x) is the Heaviside step function with h(x > 0) = 1 and h(x > 0) = 0 (not to be confused with Planck s constant). The limit a(J.. . ) indicates that the sunnnation is restricted to channel potentials witir a given set of good quantum numbers (J.. . ). 

Contrary to the impression that one might have from a traditional course in introductory calculus, well-behaved functions that cannot be integrated in closed form are not rare mathematical curiosities. Examples are the Gaussian or standard error function and the related function that gives the distribution of molecular or atomic speeds in spherical polar coordinates. The famous blackbody radiation cuiwe, which inspired Planck s quantum hypothesis, is not integrable in closed form over an arbitiar y inteiwal. 

Modern physics dates from Planck s proposal that en ergy IS quantized which set the stage for the develop ment of quantum mechanics Planck received the 1918 No bel Prize in physics... 

Electromagnetic radiation of which visible light is but one example has the properties of both particles and waves The particles are called photons, and each possesses an amount of energy referred to as a quantum In 1900 the German physicist Max Planck proposed that the energy of a photon (E) is directly proportional to its frequency (v)... 

Classical and Quantum Mechanics. At the beginning of the twentieth century, a revolution was brewing in the world of physics. For hundreds of years, the Newtonian laws of mechanics had satisfactorily provided explanations and supported experimental observations in the physical sciences. However, the experimentaUsts of the nineteenth century had begun delving into the world of matter at an atomic level. This led to unsatisfactory explanations of the observed patterns of behavior of electricity, light, and matter, and it was these inconsistencies which led Bohr, Compton, deBroghe, Einstein, Planck, and Schrn dinger to seek a new order, another level of theory, ie, quantum theory. 

In the process of excitation, the dye molecule absorbs a quantum of uv or visible radiation. The quantum has an energy E = hv, where b is Planck s constant and O is the frequency of the radiation. The higher the frequency of the quantum, the shorter the wavelength X, with u-A = c, where c is the velocity of light in a vacuum. 

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