Quantum hypothesis

This is known as the Stefan-Boltzmaim law of radiation. If in this calculation of total energy U one uses the classical equipartition result = k T, one encounters the integral f da 03 which is infinite. This divergence, which is the Rayleigh-Jeans result, was one of the historical results which collectively led to the inevitability of a quantum hypothesis. This divergence is also the cause of the infinite emissivity prediction for a black body according to classical mechanics. 

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. 

Quantenhypothese, /. quantum hypothesis, quantenmassig, a. pertaining to quanta, in relation to quanta. 

Liapounov theorems for stability and instability, 346, 347, 348 Lienard, A., 334 Ufskitz, E. M., 726,759,768 Light quantum hypothesis, 485 Limit cycles, 328 coalescence of, 339 stable, 329 unstable, 329 Lindsay, R. ., 4,47 Lindstedt method of eliminating secular terms, 349... 

The result of this collaboration was the repetition by Mark and his associate, Hartmut Kallmann, of A. H. Compton s famous confirmation of Einstein s light-quantum hypothesis (15,16). 

Laboratory. During the period 19191922, Langmuir developed what he called a "deductive chemistry" using the electron-pair theory of valency and the quantum hypothesis. However, physicists rejected the premises and methodology of Langmuir s theory, which proposed the existence of a "quantum force" to counterbalance Coulombic attraction and which used the notion of principal quantum number but deduced positions of equilibrium rather than quantum jumps for electrons. 12... 

The second two terms of the sum (711) can be eliminated using a combination of the free-photon minimal prescription and the quantum hypothesis... 

Niels Bohr Used the Quantum Hypothesis to Explain Atomic Spectra... 

NIELS BOHR USED THE QUANTUM HYPOTHESIS TO EXPLAIN ATOMIC SPECTRA... 

Bohr s planetary atomic model proved to be a tremendous success. By utilizing Planck s quantum hypothesis, Bohr s model solved the mystery of atomic spectra. Despite its successes, though, Bohr s model was limited because it did not explain why energy levels in an atom are quantized. Bohr himself was quick to point out that his model was to be interpreted only as a crude beginning, and the picture of electrons whirling about the nucleus like planets about the sun was not to be taken literally (a warning to which popularizers of science paid no heed). 

Quantum hypothesis The idea that light energy is contained in discrete packets called quanta. 

There are several reasons for starting this account with a discussion of electromagnetic radiation. Historically, it was in this area that the quantum theory first developed. It is easier here to understand the evidence for the theory, and to appreciate some of its paradoxical consequences, than it is in the quantum theory of matter. The applications of the light-quantum hypothesis, as it was first called, also provide key pieces of evidence for the quantization of energy in atoms and molecules. Studies of the absorption and emission of radiation—the field of spectroscopy—and of the effect of light on chemical reactions—photochemistry—are very important areas of modem chemistry, in which the quantum nature of radiation is crucial. 

Planck is of opinion that the assumption that the entropy is always a positive quantity, and hence that the probabihty is always an integer, is equivalent to the so-caUed quantum hypothesis. ... 

Planck s law represents the experimental facts better than any other law which has yet been proposed, and is probably accurate to within the experimental errors. The quantum hypothesis has also proved very fruitful in other branches of physics. The question of the distribution law cannot, however, even yet be regarded as definitely settled. 

To Einstein is due the credit of having been the first to point out that, apart from the law of heat radiation, there are other phenomena which can be explained by means of the quantum hypothesis, but which are unintelligible from the standpoint of classical physics. In the year 1905, Einstein put forward the light quantum hypothesis, and as experimental evidence for it cited the law of the photoelectric effect this we have already dealt with ( 2, p. 69). 

We can also try to deduce the radiation formula, not as above from the pure wave standpoint by quantisation of the cavity radiation, but from the standpoint of the theory of light quanta, that is to say, of a corpuscular theory. For this we must therefore develop the statistics of the light-quantum gas, and the obvious suggestion is to apply the methods of the classical Boltzmann statistics, as in the kinetic theory of gases the quantum hypothesis, introduced by Planck in his treatment of cavity radiation by the wave method, is of course taken care of from the first in the present case, in virtue of the fact that we are dealing with light quanta, that is, with particles (photons) with energy hv and momentum Av/c. It turns out, however, that the attempt to deduce Planck s radiation law on these lines also fails, as we proceed to explain. 

The roots of core and valence level photoemission can be tracked back to the famous article of Einstein explaining the photoelectric effect.164 In this work, he postulated the quantum hypothesis for absorption of radiation by the fundamental equation ... 

The regions of the presynaptic membrane where fusion of vesicles and the plasmalemma occur are limited to what has been termed the active zones. Closely associated with these active zones are what electron microscopists believe may be clusters of calcium ionophores necessarv for the entry of Ca + for the initiation of exocytotic release. Other morphological entities at the active zone have also been identified, but their physiological role in transmitter release has not been elucidated. It should be noted that numerous freeze-fracture micrographs taken of active synapses reveal many more vesicle fusions than would be predicted for one or two release events. These observations are not consistent with the one vesicle-one quantum hypothesis that was briefly discussed earlier. To date, no explanation for the discrepancy between the number of vesicles and the number of quanta released has been proposed except to suggest that the vesicle, in fact, only releases a fraction of the quantum, which has been termed a microquantum. 

It is commonly accepted that the old quantum theory era spans from the birth of Planck s quantum hypothesis to the formulation of Schrodinger s equation. This section describes the old quantum theory in three parts the failure of classical mechanics, the birth of the quantum theory, and the completion of wave mechanics.5 8) This century obviously began with the birth of quantum theory. Many researchers appeared on the scene of quantum theory at the time, but we remember mostly the contributions of four researchers Max Planck (1901), Albert Einstein (1905), Niels Bohr (1913), and de Broglie (1923). Then Schrodinger proposed the new wave equation to conclude the age of the old quantum theory. Heisenberg established matrix mechanics and formulated the uncertainty principle. 

There is no question that the three reports, the photoelectric effect, the special relativity and the Brownian motion published by Einstein in 1905 changed the traditional consciousness of researchers in the 20th century. The report on the photoelectric effect clarified an old problem in the wave theory of light by linking discussions on the nature of light and the quantum hypothesis originating in Planck s study of specific heat. The report on special relativity refuted the ether theory and created an entirely new field. The report on Brownian motion, aimed at the very existence of atoms and molecules, created the theory... 

The development of the quantum theory began with Planck s quantum hypothesis and... 

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