Sir William Rowan Hamilton (August 4, 1805 – September 2, 1865) was an Irish mathematician, physicist, and astronomer who made important contributions to the development of optics, dynamics, and algebra. His discovery of quaternions is perhaps his best known investigation. Hamilton's work in dynamics was later significant in the development of quantum mechanics, where a fundamental concept called the Hamiltonian bears his name. Hamilton showed immense talent at a very early age, prompting Dr. John Brinkley, astronomer and bishop of ...
Canonical is an adjective derived from canon. It essentially means "standard", "generally accepted" or "part of the back-story."
basic, canonic, canonical: reduced to the simplest and most significant form possible without loss of generality, e.g. "a basic story line"; "a canonical syllable pattern"
Canonical - Religion.
This word is used by theologians and canon lawyers to refer to the canons of the Eastern Orthodox and Roman Catholic churches, adopted by ecumenical councils.
Classical physics is physics based on principles developed before the rise of quantum theory, including the special theory of relativity. (In contrast, modern physics refers to the physicist's world view wrought by the revolutionary quantum theory.) There are no restrictions on the application of classical principles, but, practically, the scale of classical physics is the level of isolated atoms and molecules on upwards, including the macroscopic and astronomical realm. Inside the atom and among atoms in a molecule, the laws o ...
In thermodynamics and statistical mechanics, the thermodynamic entropy (or simply the entropy) S is a key physical variable in describing a thermodynamic system.
The SI unit of entropy is J·K−1 (joules per kelvin), which is the same as the unit of heat capacity, and entropy is said to be thermodynamically conjugate to temperature. The entropy depends only on the current state of the system, not its detailed previous history, and so it is a state function of the parameters like pressure, temperature, etc., which describe the ob ...
In mathematics and physics, continuous spectrum is, roughly speaking, a non-countable set of eigenvalues of an operator. An operator acting on a Hilbert space is said to have a continuous spectrum if its eigenvalues can be changed continuously. If the spectrum of an operator is not continuous, we say that it is has discrete spectrum. Some of the basic questions in spectral theory are to characterise the discrete spectrum and purely continuous spectrum, just as a measure, such as a probability measure, can typically ...
In physics, a virtual particle is a loosely defined term that is frequently used to explain or illuminate a variety of disparate effects in quantum field theory. It usually refers to a field excitation mode that appears in an intermediate step in a calculation. The terms off-shell, off-shell particle or off-shell excitation are also commonly used. The term is used as a contrast with the idea of a real particleIncluding:
See Cartesian coordinate system or Coordinates (mathematics) for a more elementary introduction to this topic.
In mathematics as applied to geometry, physics or engineering, a coordinate system is a system for assigning a tuple of numbers to each point in an n-dimensional space. "Numbers" in many cases means real numbers, but, depending on context, can mean complex numbers or elements of some other field. If the space or manifold is curved, it may not be possible to provide one consistent coordinate system for the entire space. In this case, a set of coordinate systems, called charts, are ...
In mathematics and physics, unitarity is the property of an operator (or a matrix) that is unitary.
In physics, the requirement of unitarity of the evolution operator or the S-matrix (the evolution operator from to ) is essential for the physical interpretation of any complete theory. These operators must preserve the squared length of the original vector in the Hilbert space simply because the physical interpretation of this squared length, according to the basic principles of quantum mechanics, is the total probability of al ...
The Republican Party, often called the GOP (for "Grand Old Party"), is one of the two major political parties in the United States, the other being the Democratic Party. The party was first established in 1854 by Northerners who were opposed to the spread of slavery, and held a Hamiltonian vision for modernizing the nation. In the modern political era, the GOP is usually considered the more socially conservative and economically neoliberal of the two major parties.
The current President, George W. Bush, is the party lead ...
In quantum gauge theories, in the Hamiltonian formulation, the wave function is a functional of the gauge connection A and matter fields φ. Being a quantum gauge theory, we have to impose first class constraints in the form of functional differential equations. Basically, the Gauss constraint.
In flat spacetime, space is noncompact R3. Since the Gauss constaints are local, it suffices to consider gauge transformations U which approach 1 at spatial infinity. Alternatively, we can assume space is an very large three s ...
Quantum mechanics is a fundamental physical theory that replaces Newtonian mechanics and classical electromagnetism at the atomic and subatomic levels and is the underlying framework of many fields of physics and chemistry, including condensed matter physics, quantum chemistry, and particle physics. Along with general relativity, it is one of the pillars of modern physics.
Quantum mechanics - Introduction.
The term quantum (Latin, "how much") refers to the discrete units that the theory assign ...
In physics, the Schrödinger equation, proposed by the Austrian physicist Erwin Schrödinger in 1925, describes the time-dependence of quantum mechanical systems. It is of central importance to the theory of quantum mechanics, playing a role analogous to Newton's second law in classical mechanics.
In the mathematical formulation of quantum mechanics, each system is associated with a complex Hilbert space such that each instantaneous state of the system is described by a unit vector in that space. This state vector encodes the p ...
The wave packet is one of the most widely misunderstood and misused concepts in physics. In general, a wave packet is an envelope or packet containing an arbitrary number of wave forms. This is also true in quantum mechanics, however in this case the wave packet is ascribed a special significance. In quantum mechanics the wave packet is interpreted to be a "probability wave" describing the probability that a particu ...
Computational chemistry is a branch of theoretical chemistry whose major goals are to create efficient mathematical approximations and computer programs that calculate the properties of molecules (such as total energy, dipole and quadrupole moment, vibrational frequencies, reactivity and other diverse spectroscopic quantitities and cross sections for collision of molecules with diverse atomic or subatomic projectiles) and to apply these programs to concrete chemical objects. The term is also sometimes used to cover the areas of overla ...
Corresponding to each kind of particle, there is an associated antiparticle with the same mass and spin. Some particles, such as the photon, are identical to their antiparticle; such particles must have no electric charge, but not all charge-neutral particles are of this kind. The laws of nature were thought to be symmetric between particles and antiparticles until CP violation experiments found that time-reversal symmetry is violated in nature. The observed excess of baryons over anti-baryons in the universe is ...
In mathematics and physics, the canonical coordinates are a special set of coordinates on the cotangent bundle of a manifold. They are usually written as a set of (qi,pj) or (xi,pj) with the x 's or q 's denoting the coordinates on the underlying manifold and the p 's denoting the conjugate momentum, which are 1-forms in the cotangent bundle at point < ...
In physics, the Casimir effect is a weak force exerted between seperate objects, which is not due to charge, gravity, or exchange of particles, but instead is due to resonance in the intervening space between the objects, of all-pervasive energy fields. The force is only measurable when the distance between the objects is extremely small, since it falls off rapidly with distance.
Dutch physicist Hendrik B. G. Casimir first proposed the exitence of the force, and an experiment to detect it in 1948 whil ...
Archibald Campbell, 1st Marquess of Argyll and 8th Earl of Argyll (1607 - 27 May 1661) was the de facto head of government in Scotland during most of the Scottish Civil War (which was part of the Wars of the Three Kingdoms).
He was eldest son of Archibald, 7th Earl, by his first wife, was educated at St Andrews University, where he matriculated on 15 January 1622. He had early in life, as Lord Lorne, been entrusted with the possession of the Argyll estates when his father renounced Protestantism and took arms for Philip ...
An annihilation operator is the operator in that lowers the number of particles in a given state by one. A creation operator is an operator that increases the number of particles in a given state by one, and it is the adjoint of the annihilation operator. Depending on the context, the identity of the particles in question varies, i.e. in quantum chemistry , and many-body theory the creation and annihilation operators often act on electrons. Annihilation and creation operators can also refer specifically to the ladder operators ...
A less formal description of the electrons in atoms can be found at Electron configuration.
In quantum mechanics, the state of an atom, i.e. the eigenstates of the atomic Hamiltonian, are expanded (see configuration interaction expansion and basis (linear algebra)) into linear combinations of anti-symmetrized products (Slater determinants) of one-electron functions. The spatial components of these one-electron functions are called atomic orbitals. (When one considers also their spin c ...
