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.

Thermodynamics

2017 ◽  
Author(s):  
Nicholas Manton ◽  
Nicholas Mee
Keyword(s):  
Chemical Potential ◽  
Black Body ◽  
Black Body Radiation ◽  
Spin Systems ◽  
Atomic Scale ◽  
Einstein Condensation ◽  
Maxwell Distribution ◽  
Bose Einstein Condensation ◽  
Thermodynamic Variables ◽  
Bose Einstein

This chapter is about thermodynamics, or statistical mechanics, which explains macroscopic features of the world in terms of the motion of vast numbers of particles on the atomic scale. It discusses how macroscopic variables such as temperature and entropy were originally introduced, before presenting modern definitions of temperatures and entropy and the Laws of Thermodynamics. Alternative thermodynamic variables, including enthalpy and the Gibbs free energy, are defined and the Gibbs distribution is explained. The Maxwell distribution is derived. The chemical potential is introduced and the pressure and heat capacity of an electron gas is calculated, The Fermi–Dirac and Bose–Einstein functions are derived. Bose–Einstein condensation is explained. Black body radiation is discussed and the Planck formula is derived. Lasers are explained. Spin systems are used to model magnetization. Phase transitions are briefly discussed. Hawking radiation and the thermodynamics of black holes is explained.

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.

Recollections of early solid state physics

1980 ◽  
Vol 371 (1744) ◽  
pp. 28-38 ◽  
Keyword(s):  
State Physics ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Solid State ◽  
Particle Physics ◽  
Critical Size ◽  
Mathematical Physics ◽  
British Government ◽  
Solid State Physics ◽  
Nuclear Bomb

Peierls, Sir Rudolf Ernst. Born Berlin 1907. Studied at Berlin, Munich and Leipzig. From 1932 held research positions in Manchester and Cambridge. Was Professor of mathematical physics in Birmingham and Oxford. Knighted 1968. Author of many papers applying quantum mechanics to problems in solid state and in particle physics', author of Quantum theory of solids, 1955. Author with 0. R. Frisch in 1940 of ‘ Confidential memorandum to British Government on possibility and critical size of nuclear bomb'.

Quantum 20/20

2019 ◽  
Author(s):  
Ian R. Kenyon
Keyword(s):  
Quantum Mechanics ◽  
Hall Effect ◽  
Particle Physics ◽  
Quantum Spin ◽  
Lessons Learned ◽  
Compact Stars ◽  
Einstein Condensation ◽  
Local Conservation ◽  
Variable Theory ◽  
Quantum Gauge Theory

This text reviews fundametals and incorporates key themes of quantum physics. One theme contrasts boson condensation and fermion exclusivity. Bose–Einstein condensation is basic to superconductivity, superfluidity and gaseous BEC. Fermion exclusivity leads to compact stars and to atomic structure, and thence to the band structure of metals and semiconductors with applications in material science, modern optics and electronics. A second theme is that a wavefunction at a point, and in particular its phase is unique (ignoring a global phase change). If there are symmetries, conservation laws follow and quantum states which are eigenfunctions of the conserved quantities. By contrast with no particular symmetry topological effects occur such as the Bohm–Aharonov effect: also stable vortex formation in superfluids, superconductors and BEC, all these having quantized circulation of some sort. The quantum Hall effect and quantum spin Hall effect are ab initio topological. A third theme is entanglement: a feature that distinguishes the quantum world from the classical world. This property led Einstein, Podolsky and Rosen to the view that quantum mechanics is an incomplete physical theory. Bell proposed the way that any underlying local hidden variable theory could be, and was experimentally rejected. Powerful tools in quantum optics, including near-term secure communications, rely on entanglement. It was exploited in the the measurement of CP violation in the decay of beauty mesons. A fourth theme is the limitations on measurement precision set by quantum mechanics. These can be circumvented by quantum non-demolition techniques and by squeezing phase space so that the uncertainty is moved to a variable conjugate to that being measured. The boundaries of precision are explored in the measurement of g-2 for the electron, and in the detection of gravitational waves by LIGO; the latter achievement has opened a new window on the Universe. The fifth and last theme is quantum field theory. This is based on local conservation of charges. It reaches its most impressive form in the quantum gauge theories of the strong, electromagnetic and weak interactions, culminating in the discovery of the Higgs. Where particle physics has particles condensed matter has a galaxy of pseudoparticles that exist only in matter and are always in some sense special to particular states of matter. Emergent phenomena in matter are successfully modelled and analysed using quasiparticles and quantum theory. Lessons learned in that way on spontaneous symmetry breaking in superconductivity were the key to constructing a consistent quantum gauge theory of electroweak processes in particle physics.

Electromagnetic fluctuations from energetic particles in plasmas

1988 ◽  
Vol 40 (3) ◽  
pp. 407-417 ◽  
Author(s):  
Cheng Chu ◽  
J. L. Sperling
Keyword(s):  
Distribution Function ◽  
Velocity Distribution ◽  
Charged Particles ◽  
Velocity Distribution Function ◽  
Black Body ◽  
Black Body Radiation ◽  
Specific Model ◽  
Magnetized Plasma ◽  
Plasma Power ◽  
Correlation Techniques

Electromagnetic fluctuations, induced by energetic charged particles, are calculated using correlation techniques for a uniform magnetized plasma. Power emission in the ion-cyclotron range of frequencies (ICRF) is calculated for a specific model of velocity distribution function. The emissive spectra are distinct from that of the black-body radiation and have features that are consistent with experimental observation.

Effect of Surface Roughness on the Total Hemispherical and Specular Reflectance of Metallic Surfaces

1964 ◽  
Vol 86 (2) ◽  
pp. 193-199 ◽  
Author(s):  
R. C. Birkebak ◽  
E. M. Sparrow ◽  
E. R. G. Eckert ◽  
J. W. Ramsey
Keyword(s):  
Surface Roughness ◽  
Black Body ◽  
Black Body Radiation ◽  
The Other ◽  
Angle Of Incidence ◽  
Metallic Surfaces ◽  
Specular Reflectance ◽  
Other Hand ◽  
Hemispherical Reflectance ◽  
Effect Of Surface

Measurements have been made of the hemispherical and specular reflectance of metallic surfaces of controlled roughness. The surfaces, which were ground nickel rectangles, were irradiated at various angles of incidence by a beam of black-body radiation, the temperature of which was also varied. The instrumentation which was devised to perform the experiments is described. The measurements show that beyond a certain surface roughness, the hemispherical reflectance is virtually independent of further increases in roughness. On the other hand, the specular reflectance decreases steadily with increasing roughness. Additionally, the hemispherical reflectance is found to be quite insensitive to the angle of incidence, while the specular reflectance increases with angle of incidence for the rougher surfaces.

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