Planck-Einstein quantization

The settling of certain particular amplitude depends on the initial conditions. When the motion becomes stationary the amplitude s value practically does not depend on the wave s intensity when the latter changes over a significant range above a certain threshold value. This is reminiscent of Einstein s explanation of the photoelectric effect using Planck s quantization hypothesis. In this case the absorption is also independent of the incoming wave s intensity. Besides, the absorbed... 

The problem of specific heats, treated by Jeans from the classical point of view, as I said above, was discussed by Einstein in the case of solids, with special regard to the discrepancy observed at low temperature between the measured values and those deduced from the theory he had constructed in 1907 by quantizing the mechanical oscillators3 as Planck had quantized the radiation oscillators. 

Planck s Quantized Energies and Einstein s Photoelectric Effect... 

The photoelectric effect was explained by Albert Einstein in 1905 using the principles of quantum physics developed by Max Planck. Einstein claimed that light was quantized— that is, it appeared in bundles of energy. While these bundles traveled in waves, certain reactions (like the photoelectric effect) revealed their particulate nature. This theory was further supported in 1923 by... 

The idea that time has no objective existence but depends on events led some scientists to abandon the assumption that it is a continuous variable. Following the establishment of the Planck-Einstein quantum theory, it was suggested by Poincare and others that time is quantized one calculation gave the value 10 " s to the chronon . 

In the course of his research on electromagnetic waves Hertz discovered the photoelectric effect. He showed that for the metals he used as targets, incident radiation in the ultraviolet was required to release negative charges from the metal. Research by Philipp Lenard, Wilhelm Hallwachs, J. J. Thomson, and other physicists finally led Albert Einstein to his famous 1905 equation for the photoelectric effect, which includes the idea that electromagnetic energy is quantized in units of hv, where h is Planck s con-... 

Bohr knew of the work of Planck and Einstein. What if the energies of electrons in an atom were not continuous What if they could only take on certain values What if atoms were quantized, just as blackbody oscillators and light that struck a metal plate were. The challenge was how to apply quantum ideas to the atom. 

But it was Max Planck who shattered the paradigm of the steadiness of nature. He showed that atoms could not absorb energy in all forms and quantities, but only in so-called quanta, that is, in defined amounts. Thus, electrons jump, as we explain it today, from one energy level to another. Natura saltat Albert Einstein s theory was even more groundbreaking space and time form a continuum, matter and energy, in contrast, are quantized, essentially "grainy", so to speak. In this case, nature cannot but jump. 

Einstein (1907) applied equation 3.32 (originally conceived by Planck for the quantization of electromagnetic energy) to the quantization of particle energy, describing the internal energy of a solid composed of Nq atoms as... 

These facts were explained by Einstein5 in 1905 in a way that now appears very simple, but in fact relies on concepts that were at the time revolutionary. Einstein went beyond Planck and postulated that not only was the process of absorption and emission of light quantized, but that light itself was quantized, consisting in effect of particles of energy... 

What is not so well known about Einstein is that he made contributions to the development of modern chemistry, particularly to the area of quantum mechanics. The Nobel Prize Committee awarded Einstein the Nobel Prize in physics in 1921 for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect. His explanation of the photoelectric effect helped to validate Planck s view of quantized energy, and has become the basis of the quantitative laws of photochemistry. 

It is very well known that Einstein, developing Planck s ideas, quantized the electromagnetic field by introducing a quantum particle named the photon. Consequently, each mode or state of a classical electromagnetic field is characterized by an angular frequency, co, and a wave vector,... 

German physicist Max Planck had already suggested that energy in general was quantized, meaning that it exists in packets. Building on this idea, Einstein proposed that light could behave as particles, which he called photons. 

Planck found it necessary to assume quantized energies to explain the radiation that heated bodies emit. Einstein s analysis of the photoelectric effect used Planck s concepts, suggesting that electromagnetic radiation is quantized. 23. 3.0 x 1010 s ... 

Einstein s work extended German physicist Maxwell Planck s (1858-1947) concept of enei y quantization to electromagnetic radiation. 

Extending Planck s idea of quantized energy, Einstein calculated that a photon s energy depends on its frequency. 

The modern student, to whom the Bohr frequency rule has become commonplace, might consider that this rule is clearly evident in the work of Planck and Einstein. This is not so, however the confusing identity of the mechanical frequencies of the harmonic oscillator (the only system discussed) and the frequency of the radiation absorbed and emitted by this quantized system delayed recognition of the fact that a fundamental violation of electromagnetic theory was imperative. 

It is possible to find in the history of science many vivid examples illustrating the relativity of the concept fundamental . For instance, the Planck postulate of energy quantization and the Bohr postulate on the quantization on angular momentum made a revolution in physics and were actually axioms at that time. At present from the formal viewpoint, they are only ordinary consequences of Schroedinger s equation [4], Another vivid example is provided by the four famous Maxwell electrodynamic equations which, as was found later, can be derived from Coulomb s law and Einstein s relativity principle [5]. 

Soon after the nuclear model was proposed, Niels Bohr (1885-1962), a young Danish physicist working in Rutherford s laboratory, suggested a model for the H atom that predicted the existence of line spectra. In his model, Bohr used Planck s and Einstein s ideas about quantized energy and proposed three postulates ... 

Planck Energy is quantized only certain values allowed Einstein Light has particulate behavior (photons)... 

Understand how particles and waves differ and how the work of Planck (quantization of energy) and Einstein (photon theory) changed thinking about it ( 7.1) (EPs 73-7.5)... 

CO. If f/is viewed as divisible without limit, then an infinite number of distributions are possible. Planck considered U as made up of an entirely determined number of finite equal parts of value fia. This quantization of the electromagnetic radiation leads to the concept of photons of energy quanta fico, each of which having a Hamiltonian of the form of a harmonic oscillator. A state of the free electromagnetic field is specified by the number, n, for each of such oscillators and n then corresponds to the number of photons in a state with energy fico. Photons obey Bose-Einstein statistics. Denote by the number of photons with energy... 

Despite its successes, Bohr s theory did not resolve the fundamental issues that lie at the heart of the quantum theory of Planck and Einstein What is behind the quantization of oscillators and atoms What happens when a system changes its state, resulting in the creation of a photon How can the generated photon behave like a particle under certain conditions and like a wave under other conditions ... 

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