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Classical mechanics

Classical mechanics
Diagram of orbital motion of a satellite around the earth, showing perpendicular velocity and acceleration (force) vectors. In physics, classical mechanics and quantum mechanics are the two major sub-fields of mechanics. Classical mechanics is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces. The term classical mechanics was coined in the early 20th century to describe the system of physics begun by Isaac Newton and many contemporary 17th century natural philosophers, building upon the earlier astronomical theories of Johannes Kepler, which in turn were based on the precise observations of Tycho Brahe and the studies of terrestrial projectile motion of Galileo. The initial stage in the development of classical mechanics is often referred to as Newtonian mechanics, and is associated with the physical concepts employed by and the mathematical methods invented by Newton himself, in parallel with Leibniz, and others. Similarly,

Aerodynamics A vortex is created by the passage of an aircraft wing, revealed by smoke. Vortices are one of the many phenomena associated with the study of aerodynamics. Formal aerodynamics study in the modern sense began in the eighteenth century, although observations of fundamental concepts such as aerodynamic drag have been recorded much earlier. Most of the early efforts in aerodynamics worked towards achieving heavier-than-air flight, which was first demonstrated by Wilbur and Orville Wright in 1903. History[edit] Modern aerodynamics only dates back to the seventeenth century, but aerodynamic forces have been harnessed by humans for thousands of years in sailboats and windmills,[1] and images and stories of flight appear throughout recorded history,[2] such as the Ancient Greek legend of Icarus and Daedalus.[3] Fundamental concepts of continuum, drag, and pressure gradients, appear in the work of Aristotle and Archimedes.[4] Fundamental concepts[edit] Flow classification[edit]

Theory of relativity The theory of relativity, or simply relativity in physics, usually encompasses two theories by Albert Einstein: special relativity and general relativity.[1] Concepts introduced by the theories of relativity include: Measurements of various quantities are relative to the velocities of observers. In particular, space contracts and time dilates.Spacetime: space and time should be considered together and in relation to each other.The speed of light is nonetheless invariant, the same for all observers. The term "theory of relativity" was based on the expression "relative theory" (German: Relativtheorie) used in 1906 by Max Planck, who emphasized how the theory uses the principle of relativity. Scope[edit] The theory of relativity transformed theoretical physics and astronomy during the 20th century. In the field of physics, relativity improved the science of elementary particles and their fundamental interactions, along with ushering in the nuclear age. Two-theory view[edit] History[edit]

Old quantum theory The main tool was Bohr–Sommerfeld quantization, a procedure for selecting out certain discrete set of states of a classical integrable motion as allowed states. These are like the allowed orbits of the Bohr model of the atom; the system can only be in one of these states and not in any states in between. The theory did not extend to chaotic motions. Basic principles[edit] The basic idea of the old quantum theory is that the motion in an atomic system is quantized, or discrete. where the are the momenta of the system and the are the corresponding coordinates. are integers and the integral is taken over one period of the motion at constant energy (as described by the Hamiltonian). In order for the old quantum condition to make sense, the classical motion must be separable, meaning that there are separate coordinates in terms of which the motion is periodic. Examples[edit] Harmonic oscillator[edit] a result which was known well before, and used to formulate the old quantum condition. . . and . as

Acoustics Acoustics is the interdisciplinary science that deals with the study of all mechanical waves in gases, liquids, and solids including vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics technology may be called an acoustical engineer. The application of acoustics is present in almost all aspects of modern society with the most obvious being the audio and noise control industries. The word "acoustic" is derived from the Greek word ἀκουστικός (akoustikos), meaning "of or for hearing, ready to hear"[2] and that from ἀκουστός (akoustos), "heard, audible",[3] which in turn derives from the verb ἀκούω (akouo), "I hear".[4] The Latin synonym is "sonic", after which the term sonics used to be a synonym for acoustics[5] and later a branch of acoustics.[6] Frequencies above and below the audible range are called "ultrasonic" and "infrasonic", respectively. History of acoustics[edit]

Thermodynamics Annotated color version of the original 1824 Carnot heat engine showing the hot body (boiler), working body (system, steam), and cold body (water), the letters labeled according to the stopping points in Carnot cycle Thermodynamics applies to a wide variety of topics in science and engineering. Historically, thermodynamics developed out of a desire to increase the efficiency and power output of early steam engines, particularly through the work of French physicist Nicolas Léonard Sadi Carnot (1824) who believed that the efficiency of heat engines was the key that could help France win the Napoleonic Wars.[1] Irish-born British physicist Lord Kelvin was the first to formulate a concise definition of thermodynamics in 1854:[2] "Thermo-dynamics is the subject of the relation of heat to forces acting between contiguous parts of bodies, and the relation of heat to electrical agency." Introduction[edit] A thermodynamic system can be defined in terms of its states. History[edit] Etymology[edit]

Interference (wave propagation) Swimming Pool Interference[1] Interference of waves from two point sources. Magnified-image of coloured interference-pattern in soap-film. The black "holes" are areas where the film is very thin and there is a nearly total destructive interference. Consider, for example, what happens when two identical stones are dropped into a still pool of water at different locations. Geometrical arrangement for two plane wave interference Interference fringes in overlapping plane waves A simple form of interference pattern is obtained if two plane waves of the same frequency intersect at an angle. It can be seen that the two waves are in phase when and are half a cycle out of phase when Constructive interference occurs when the waves are in phase, and destructive interference when they are half a cycle out of phase. and df is known as the fringe spacing. The fringes are observed wherever the two waves overlap and the fringe spacing is uniform throughout. A point source produces a spherical wave. for to where

Condensed matter physics The diversity of systems and phenomena available for study makes condensed matter physics the most active field of contemporary physics: one third of all American physicists identify themselves as condensed matter physicists,[2] and The Division of Condensed Matter Physics (DCMP) is the largest division of the American Physical Society.[3] The field overlaps with chemistry, materials science, and nanotechnology, and relates closely to atomic physics and biophysics. Theoretical condensed matter physics shares important concepts and techniques with theoretical particle and nuclear physics.[4] References to "condensed" state can be traced to earlier sources. For example, in the introduction to his 1947 "Kinetic theory of liquids" book,[8] Yakov Frenkel proposed that "The kinetic theory of liquids must accordingly be developed as a generalization and extension of the kinetic theory of solid bodies. History[edit] Classical physics[edit] Advent of quantum mechanics[edit]

Statistical mechanics Statistical mechanics is a branch of mathematical physics that studies, using probability theory, the average behaviour of a mechanical system where the state of the system is uncertain.[1][2][3][note 1] The present understanding of the universe indicates that its fundamental laws are mechanical in nature, and that all physical systems are therefore governed by mechanical laws at a microscopic level. These laws are precise equations of motion that map any given initial state to a corresponding future state at a later time. A common use of statistical mechanics is in explaining the thermodynamic behaviour of large systems. Statistical mechanics also finds use outside equilibrium. Principles: mechanics and ensembles[edit] In physics there are two types of mechanics usually examined: classical mechanics and quantum mechanics. Using these two ingredients, the state at any other time, past or future, can in principle be calculated. Statistical thermodynamics[edit] Fundamental postulate[edit]

Bra-ket notation In quantum mechanics, bra–ket notation is a standard notation for describing quantum states, composed of angle brackets and vertical bars. It can also be used to denote abstract vectors and linear functionals in mathematics. It is so called because the inner product (or dot product on a complex vector space) of two states is denoted by a ⟨bra|ket⟩, consisting of a left part, ⟨φ|, called the bra /brɑː/, and a right part, |ψ⟩, called the ket /kɛt/. The notation was introduced in 1939 by Paul Dirac[1] and is also known as Dirac notation, though the notation has precursors in Grassmann's use of the notation [φ|ψ] for his inner products nearly 100 years previously.[2][3] Bra–ket notation is widespread in quantum mechanics: almost every phenomenon that is explained using quantum mechanics—including a large portion of modern physics — is usually explained with the help of bra–ket notation. Vector spaces[edit] Background: Vector spaces[edit] though the coordinates are now all complex-valued. where