Hamiltonian Mechanics Wikipedia

Hamiltonian mechanics - Wikipedia.

Hamiltonian mechanics emerged in 1833 as a reformulation of Lagrangian mechanics.Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities ? used in Lagrangian mechanics with (generalized) momenta.Both theories provide interpretations of classical mechanics and describe the same physical phenomena.. Hamiltonian mechanics has ....


Hamiltonian (quantum mechanics) - Wikipedia.

In quantum mechanics, the Hamiltonian of a system is an operator corresponding to the total energy of that system, including both kinetic energy and potential energy.Its spectrum, the system's energy spectrum or its set of energy eigenvalues, is the set of possible outcomes obtainable from a measurement of the system's total energy.Due to its close relation to the ....


Hamiltonian - Wikipedia.

Hamiltonian may refer to: . Hamiltonian mechanics, a function that represents the total energy of a system; Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system Dyall Hamiltonian, a modified Hamiltonian with two-electron nature; Molecular Hamiltonian, the Hamiltonian operator representing the energy of the electrons and nuclei in a ....


Kinetic energy - Wikipedia.

In quantum mechanics, observables like kinetic energy are represented as operators. For one particle of mass m, the kinetic energy operator appears as a term in the Hamiltonian and is defined in terms of the more fundamental momentum operator ^. The kinetic energy operator in the non-relativistic case can be written as.


Quantum state - Wikipedia.

In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution in time exhausts all that can be predicted about the system's behavior..


Wave packet - Wikipedia.

in which we may take ? = kc.The first term represents a wave propagating in the positive x-direction since it is a function of x - ct only; the second term, being a function of x + ct, represents a wave propagating in the negative x-direction.. A wave packet is a localized disturbance that results from the sum of many different wave forms.If the packet is strongly localized, more ....


Measurement in quantum mechanics - Wikipedia.

In quantum mechanics, each physical system is associated with a Hilbert space, each element of which is a wave function that represents a possible state of the physical system. The approach codified by John von Neumann represents a measurement upon a physical system by a self-adjoint operator on that Hilbert space termed an "observable".: 17 These observables play the ....


Exchange interaction - Wikipedia.

In chemistry and physics, the exchange interaction (with an exchange energy and exchange term) is a quantum mechanical effect that only occurs between identical particles.Despite sometimes being called an exchange force in an analogy to classical force, it is not a true force as it lacks a force carrier.. The effect is due to the wave function of indistinguishable particles being subject ....


Quantum tunnelling - Wikipedia.

Quantum tunneling falls under the domain of quantum mechanics: the study of what happens at the quantum scale.Tunneling cannot be directly perceived. Much of its understanding is shaped by the microscopic world, which classical mechanics cannot explain. To understand the phenomenon, particles attempting to travel across a potential barrier can be compared to a ball ....


Casimir effect - Wikipedia.

In quantum field theory, the Casimir effect is a physical force acting on the macroscopic boundaries of a confined space which arises from the quantum fluctuations of the field. It is named after the Dutch physicist Hendrik Casimir, who predicted the effect for electromagnetic systems in 1948.. In the same year, Casimir together with Dirk Polder described a similar effect ....


Observer effect (physics) - Wikipedia.

In physics, the observer effect is the disturbance of an observed system by the act of observation. This is often the result of instruments that, by necessity, alter the state of what they measure in some manner. A common example is checking the pressure in an automobile tire; this is difficult to do without letting out some of the air, thus changing the pressure. Similarly, seeing non ....


Inertial frame of reference - Wikipedia.

In classical physics and special relativity, an inertial frame of reference is a frame of reference that is not undergoing acceleration.In an inertial frame of reference, a physical object with zero net force acting on it moves with a constant velocity (which might be zero)--or, equivalently, it is a frame of reference in which Newton's first law of motion holds..


Answer set programming - Wikipedia.

Answer set programming (ASP) is a form of declarative programming oriented towards difficult (primarily NP-hard) search problems.It is based on the stable model (answer set) semantics of logic programming.In ASP, search problems are reduced to computing stable models, and answer set solvers--programs for generating stable models--are used to perform search..


Density matrix - Wikipedia.

In quantum mechanics, a density matrix is a matrix that describes the quantum state of a physical system. It allows for the calculation of the probabilities of the outcomes of any measurement performed upon this system, using the Born rule.It is a generalization of the more usual state vectors or wavefunctions: while those can only represent pure states, density ....


Trajectory - Wikipedia.

A trajectory or flight path is the path that an object with mass in motion follows through space as a function of time. In classical mechanics, a trajectory is defined by Hamiltonian mechanics via canonical coordinates; hence, a complete trajectory is defined by position and momentum, simultaneously.. The mass might be a projectile or a satellite. For example, it can be an orbit -- ....


Continuum mechanics - Wikipedia.

Continuum mechanics is a branch of mechanics that deals with the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such models in the 19th century..


Stationary-action principle - Wikipedia.

The stationary-action principle - also known as the principle of least action - is a variational principle that, when applied to the action of a mechanical system, yields the equations of motion for that system. The principle states that the trajectories (i.e. the solutions of the equations of motion) are stationary points of the system's action functional..