Black-Body Radiation

2019 ◽  
pp. 322-330
Author(s):  
Robert H. Swendsen
Keyword(s):  
Quantum Mechanics ◽  
Energy Spectrum ◽  
Electromagnetic Radiation ◽  
Black Body ◽  
Black Body Radiation ◽  
Perfect Absorber ◽  
Max Planck ◽  
Planck’S Constant ◽  
Light Waves ◽  
Planck's Constant

A black body is a perfect absorber of electromagnetic radiation. The energy spectrum was correctly calculated by Max Planck under the assumption that the energy of light waves only came in discrete multiples of a constant (called Planck’s constant) times the frequency. This was perhaps the first achievement of quantum mechanics. The derivation is presented here. The purpose of the current chapter is to calculate the spectrum of radiation emanating from a black body. The calculation was originally carried out by Max Planck in 1900 and published the following year. This was before quantum mechanics had been invented, or perhaps it could be regarded the first step in its invention.

The Physical World

2017 ◽  
Author(s):  
Nicholas Manton ◽  
Nicholas Mee
Keyword(s):  
Quantum Mechanics ◽  
Particle Physics ◽  
Variational Principles ◽  
Black Body ◽  
Black Body Radiation ◽  
Physical World ◽  
Atomic Scale ◽  
Solid State Physics ◽  
Least Action ◽  
Dimensional Spacetime

The book is an inspirational survey of fundamental physics, emphasizing the use of variational principles. Chapter 1 presents introductory ideas, including the principle of least action, vectors and partial differentiation. Chapter 2 covers Newtonian dynamics and the motion of mutually gravitating bodies. Chapter 3 is about electromagnetic fields as described by Maxwell’s equations. Chapter 4 is about special relativity, which unifies space and time into 4-dimensional spacetime. Chapter 5 introduces the mathematics of curved space, leading to Chapter 6 covering general relativity and its remarkable consequences, such as the existence of black holes. Chapters 7 and 8 present quantum mechanics, essential for understanding atomic-scale phenomena. Chapter 9 uses quantum mechanics to explain the fundamental principles of chemistry and solid state physics. Chapter 10 is about thermodynamics, which is built around the concepts of temperature and entropy. Various applications are discussed, including the analysis of black body radiation that led to the quantum revolution. Chapter 11 surveys the atomic nucleus, its properties and applications. Chapter 12 explores particle physics, the Standard Model and the Higgs mechanism, with a short introduction to quantum field theory. Chapter 13 is about the structure and evolution of stars and brings together material from many of the earlier chapters. Chapter 14 on cosmology describes the structure and evolution of the universe as a whole. Finally, Chapter 15 discusses remaining problems at the frontiers of physics, such as the interpretation of quantum mechanics, and the ultimate nature of particles. Some speculative ideas are explored, such as supersymmetry, solitons and string theory.

Constructing Quantum Mechanics

2019 ◽  
Author(s):  
Anthony Duncan ◽  
Michel Janssen
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Stark Effect ◽  
Zeeman Effect ◽  
Black Body ◽  
Black Body Radiation ◽  
Wave Mechanics ◽  
Specific Heats ◽  
Old Quantum Theory ◽  
Upper Level

This is the first of two volumes on the genesis of quantum mechanics. It covers the key developments in the period 1900–1923 that provided the scaffold on which the arch of modern quantum mechanics was built in the period 1923–1927 (covered in the second volume). After tracing the early contributions by Planck, Einstein, and Bohr to the theories of black‐body radiation, specific heats, and spectroscopy, all showing the need for drastic changes to the physics of their day, the book tackles the efforts by Sommerfeld and others to provide a new theory, now known as the old quantum theory. After some striking initial successes (explaining the fine structure of hydrogen, X‐ray spectra, and the Stark effect), the old quantum theory ran into serious difficulties (failing to provide consistent models for helium and the Zeeman effect) and eventually gave way to matrix and wave mechanics. Constructing Quantum Mechanics is based on the best and latest scholarship in the field, to which the authors have made significant contributions themselves. It breaks new ground, especially in its treatment of the work of Sommerfeld and his associates, but also offers new perspectives on classic papers by Planck, Einstein, and Bohr. Throughout the book, the authors provide detailed reconstructions (at the level of an upper‐level undergraduate physics course) of the cental arguments and derivations of the physicists involved. All in all, Constructing Quantum Mechanics promises to take the place of older books as the standard source on the genesis of quantum mechanics.

DOES LIOUVILLE'S THEOREM IMPLY QUANTUM MECHANICS?

1999 ◽  
Vol 13 (02) ◽  
pp. 161-189
Author(s):  
C. SYROS
Keyword(s):  
Quantum Mechanics ◽  
Radiation Spectrum ◽  
Black Body ◽  
Boltzmann Distribution ◽  
Black Body Radiation ◽  
Planck Constant ◽  
Klein Gordon ◽  
Energy Variable ◽  
Liouville’S Theorem ◽  
Liouville’S Equation

The essentials of quantum mechanics are derived from Liouville's theorem in statistical mechanics. An elementary solution, g, of Liouville's equation helps to construct a differentiable N-particle distribution function (DF), F(g), satisfying the same equation. Reality and additivity of F(g): (i) quantize the time variable; (ii) quantize the energy variable; (iii) quantize the Maxwell–Boltzmann distribution; (iv) make F(g) observable through time-elimination; (v) produce the Planck constant; (vi) yield the black-body radiation spectrum; (vii) support chronotopology introduced axiomatically; (viii) the Schrödinger and the Klein–Gordon equations follow. Hence, quantum theory appears as a corollary of Liouville's theorem. An unknown connection is found allowing the better understanding of space-times and of these theories.

Effect of electromagnetic radiation on the Lamb shift

1952 ◽  
Vol 214 (1116) ◽  
pp. 137-142 ◽  
Keyword(s):  
Electromagnetic Radiation ◽  
Radiation Field ◽  
Lamb Shift ◽  
Black Body ◽  
Black Body Radiation ◽  
External Radiation ◽  
Discrete States ◽  
The Continuum

If there is an external radiation field surrounding the atom, it influences the value of the Lamb shift. It is shown that for black-body radiation at temperature comparable to 10 5 degrees, the change in the Lamb shift due to the influence of radiation is of the same order as the Lamb shift itself. Whereas the transitions to the continuum largely contribute to the Lamb shift (in the absence of radiation), the change in the Lamb shift is largely due to transitions to discrete states.

Mass gap problem and Planck constant

2021 ◽  
Vol 34 (3) ◽  
pp. 385-388
Author(s):  
Amrit S. Šorli ◽  
Štefan Čelan
Keyword(s):  
Quantum Mechanics ◽  
Einstein Relation ◽  
Planck Constant ◽  
Planck’S Constant ◽  
Mass Gap ◽  
Planck's Constant

The mass gap problem is about defining the constant that defines the minimal excitation of the vacuum. Planck’s constant is defining the minimal possible excitation of the vacuum from the point of quantum mechanics. The mass gap problem can be solved in quantum mechanics by the formulation of the photon’s mass according to the Planck‐Einstein relation.

Heisenberg, Bohr, Robertson, and the Uncertainty Principle

2020 ◽  
pp. 133-156
Author(s):  
Jim Baggott
Keyword(s):  
Quantum Mechanics ◽  
Uncertainty Principle ◽  
Laboratory Experiments ◽  
Space Time ◽  
Spectral Lines ◽  
Planck’S Constant ◽  
Classical Space ◽  
Planck's Constant

From the outset, Heisenberg had resolved to eliminate classical space-time pictures involving particles and waves from the quantum mechanics of the atom. He had wanted to focus instead on the properties actually observed and recorded in laboratory experiments, such as the positions and intensities of spectral lines. Alone in Copenhagen in February 1927, he now pondered on the significance and meaning of such experimental observables. Feeling the need to introduce at least some form of ‘visualizability’, he asked himself some fundamental questions, such as: What do we actually mean when we talk about the position of an electron? He went on to discover the uncertainty principle: the product of the ‘uncertainties’ in certain pairs of variables—called complementary variables—such as position and momentum cannot be smaller than Planck’s constant h (now h / 4π‎).

The expression E = h × f is misleading because it implies the distribution of a photon quantum over 299 792 458 m, while the expression E = (h × c)/λ enables us to explain the particle-wave duality

2021 ◽  
Vol 34 (4) ◽  
pp. 564-577
Author(s):  
Reiner Georg Ziefle
Keyword(s):  
Electromagnetic Wave ◽  
Electromagnetic Radiation ◽  
Physical Phenomenon ◽  
Planck’S Constant ◽  
Beam Splitters ◽  
Quantum Objects ◽  
Planck's Constant

The two equations E = h × f and E = (h × c)/λ for the quantum of energy of electromagnetic radiation provide the same result but describe electromagnetic radiation very differently. E = (h × c)/λ describes the quantum of energy of electromagnetic radiation to be located already in one wavelength and therefore like a particle. E = h × f describes the quantum of energy distributed over 299 792 458 m and therefore like a wave. To obtain h × f for the quantum of energy, we have to refer the quantum of energy to 299 792 458 m. Only then we obtain from E = (h × c)/(299 792 458 m), as the distance of 299 792 458 m of the velocity c is cancelling out now, E = h × 1/s = h × Hz, which is the precondition to obtain the correct value for the quantum of energy by multiplying Planck’s constant h by the frequency f. This already indicates the necessity of today's physics to have to speak of a particle-wave duality. It turns out that electromagnetic radiation consists of the first wavelength that carries the quantum of energy and behaves like a particle, which today is called “photon,” and a few following wavelengths that do not carry a further quantum of energy and behave like a wave, which today is called “electromagnetic wave.” By this knowledge, the particle-wave duality vanishes, and we obtain one single physical phenomenon, which I call “photon-wave.” The strange behavior of quantum objects at a single slit, at double-slits, and at beam splitters can now be understood in a causal way. “God does not play dice!” Einstein was right.

New test of quantum mechanics: Is Planck’s constant unique?

1991 ◽  
Vol 66 (3) ◽  
pp. 256-259 ◽  
Author(s):  
Ephraim Fischbach ◽  
Geoffrey L. Greene ◽  
Richard J. Hughes
Keyword(s):  
Quantum Mechanics ◽  
Planck’S Constant ◽  
Planck's Constant

scholarly journals AN ENTROPIC PICTURE OF EMERGENT QUANTUM MECHANICS

2012 ◽  
Vol 09 (05) ◽  
pp. 1250048 ◽  
Author(s):  
D. ACOSTA ◽  
P. FERNÁNDEZ DE CÓRDOBA ◽  
J. M. ISIDRO ◽  
J. L. G. SANTANDER
Keyword(s):  
Quantum Mechanics ◽  
Quantum Mechanical ◽  
Entropy Flow ◽  
Planck’S Constant ◽  
Formal Derivation ◽  
Usual Quantum ◽  
Holographic Screen ◽  
Holographic Screens ◽  
Planck's Constant ◽  
Emergent Quantum Mechanics

Quantum mechanics emerges à la Verlinde from a foliation of ℝ3 by holographic screens, when regarding the latter as entropy reservoirs that a particle can exchange entropy with. This entropy is quantized in units of Boltzmann's constant kB. The holographic screens can be treated thermodynamically as stretched membranes. On that side of a holographic screen where spacetime has already emerged, the energy representation of thermodynamics gives rise to the usual quantum mechanics. A knowledge of the different surface densities of entropy flow across all screens is equivalent to a knowledge of the quantum-mechanical wavefunction on ℝ3. The entropy representation of thermodynamics, as applied to a screen, can be used to describe quantum mechanics in the absence of spacetime, that is, quantum mechanics beyond a holographic screen, where spacetime has not yet emerged. Our approach can be regarded as a formal derivation of Planck's constant ℏ from Boltzmann's constant kB.

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