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skippy1729
Can Planck's law be derived from QED and statistical mechanics? Any references appreciated.
Skippy
Skippy
Yes it can. Seeskippy1729 said:Can Planck's law be derived from QED and statistical mechanics? Any references appreciated.
Demystifier said:Yes it can. See
J. J. Sakurai, Advanced Quantum Mechanics,
the end of Sec. 2.4 (pages 46-47).
Well, before these two pages Sakurai makes other derivations on emission and absorption which he uses also for other purposes. So, the full derivation takes more than two pages. But it's all there in the book.skippy1729 said:Really? In two pages? Sorry if I am skeptical but I am already into my 2014 book budget and I live hundreds of miles from a real library.
I am looking for something that starts with fundamental emission, absorbtion and scattering processes with minimal "hand waving". Is Sakuri going to do this? I tried google books and Amazon but they don't have a preview.
Demystifier said:Here is one mechanism I am aware of. Atoms are not at rest, but have a velocity due to the thermal motions. The spectrum of kinetic energies due to the atom motion is continuous. The total energy is the sum of this kinetic energy and the usual discrete energy of electron levels. Of course, this effect is larger at higher temperatures.
I believe the answer to that is that the carbon atoms are strongly perturbed by their environment, so the energies of emission are not restricted to those of isolated carbon.skippy1729 said:But what is the mechanism whereby a hot lump of coal will glow and emit photons with frequencies not in the discrete spectrum of carbon?
Planck's Law, also known as Planck's blackbody radiation law, is a fundamental equation in physics that describes the spectral energy density of electromagnetic radiation emitted by a blackbody at a given temperature.
Max Planck, a German physicist, is credited with deriving Planck's Law in 1900. His work marked a significant turning point in the field of quantum mechanics.
Planck's Law is significant because it provided a theoretical explanation for the observed spectrum of radiation emitted by blackbodies, which had previously been a puzzle for scientists. It also led to the development of quantum mechanics and the understanding of the discrete nature of energy.
Planck's Law is derived using thermodynamics and statistical mechanics principles. It involves the quantization of energy and the assumption that the blackbody radiation is in thermal equilibrium with its surroundings.
Planck's Law has various applications in fields such as astrophysics, cosmology, and materials science. It is used to understand the behavior of blackbodies, the thermal radiation from stars and galaxies, and the properties of materials at different temperatures. It also plays a crucial role in the development of technologies such as thermal imaging and solar panels.