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A **time of flight (TOF) detector** is a particle detector which can discriminate between a lighter and a heavier elementary particle of same momentum using their time of flight between two scintillators. The first of the scintillators activates a clock upon being hit while the other stops the clock upon being hit. If the two masses are denoted by and and have velocities and then the time of flight difference is given by

In experimental and applied particle physics, nuclear physics, and nuclear engineering, a **particle detector**, also known as a **radiation detector**, is a device used to detect, track, and/or identify ionizing particles, such as those produced by nuclear decay, cosmic radiation, or reactions in a particle accelerator. Detectors can measure the particle energy and other attributes such as momentum, spin, charge, particle type, in addition to merely registering the presence of the particle.

In particle physics, an **elementary particle** or **fundamental particle** is a subatomic particle with no sub structure, thus not composed of other particles. Particles currently thought to be elementary include the fundamental fermions, which generally are "matter particles" and "antimatter particles", as well as the fundamental bosons, which generally are "force particles" that mediate interactions among fermions. A particle containing two or more elementary particles is a *composite particle*.

A **scintillator** is a material that exhibits scintillation, the property of luminescence, when excited by ionizing radiation. Luminescent materials, when struck by an incoming particle, absorb its energy and scintillate. Sometimes, the excited state is metastable, so the relaxation back down from the excited state to lower states is delayed : the process then corresponds to either one of two phenomena, depending on the type of transition and hence the wavelength of the emitted optical photon: delayed fluorescence or phosphorescence, also called after-glow.

where is the distance between the scintillators. The approximation is in the relativistic limit at momentum and denotes the speed of light in vacuum.

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In physics, **angular momentum** is the rotational equivalent of linear momentum. It is an important quantity in physics because it is a conserved quantity—the total angular momentum of a system remains constant unless acted on by an external torque.

In quantum mechanics, a **Hamiltonian** is an operator corresponding to the sum of the kinetic energies plus the potential energies for all the particles in the system. It is usually denoted by *H*, also *Ȟ* or *Ĥ*. Its spectrum is the set of possible outcomes when one measures the total energy of a system. Because of its close relation to the time-evolution of a system, it is of fundamental importance in most formulations of quantum theory.

In Newtonian mechanics, **linear momentum**, **translational momentum**, or simply **momentum** is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction in three-dimensional space. If *m* is an object's mass and **v** is the velocity, then the momentum is

In quantum mechanics, the **particle in a box** model describes a particle free to move in a small space surrounded by impenetrable barriers. The model is mainly used as a hypothetical example to illustrate the differences between classical and quantum systems. In classical systems, for example, a particle trapped inside a large box can move at any speed within the box and it is no more likely to be found at one position than another. However, when the well becomes very narrow, quantum effects become important. The particle may only occupy certain positive energy levels. Likewise, it can never have zero energy, meaning that the particle can never "sit still". Additionally, it is more likely to be found at certain positions than at others, depending on its energy level. The particle may never be detected at certain positions, known as spatial nodes.

In physics, **spacetime** is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams can be used to visualize relativistic effects such as why different observers perceive *where* and *when* events occur.

The **kinetic theory of gases** describes a gas as a large number of submicroscopic particles, all of which are in constant, rapid, random motion. The randomness arises from the particles' many collisions with each other and with the walls of the container.

An **elastic collision** is an encounter between two bodies in which the total kinetic energy of the two bodies remains the same. In an ideal, perfectly elastic collision, there is no net conversion of kinetic energy into other forms such as heat, noise, or potential energy.

In special relativity, **four-momentum** is the generalization of the classical three-dimensional momentum to four-dimensional spacetime. Momentum is a vector in three dimensions; similarly four-momentum is a four-vector in spacetime. The contravariant four-momentum of a particle with relativistic energy *E* and three-momentum **p** = = *γm***v**, where **v** is the particle's three-velocity and γ the Lorentz factor, is

**Matter waves** are a central part of the theory of quantum mechanics, being an example of wave–particle duality. All matter can exhibit wave-like behavior. For example, a beam of electrons can be diffracted just like a beam of light or a water wave. The concept that matter behaves like a wave was proposed by Louis de Broglie in 1924. It is also referred to as the *de Broglie hypothesis*. Matter waves are referred to as *de Broglie waves*.

According to the theory of relativity, **time dilation** is a difference in the elapsed time measured by two observers, either due to a velocity difference relative to each other, or by being differently situated relative to a gravitational field. As a result of the nature of spacetime, a clock that is moving relative to an observer will be measured to tick slower than a clock that is at rest in the observer's own frame of reference. A clock that is under the influence of a stronger gravitational field than an observer's will also be measured to tick slower than the observer's own clock.

The **Lorentz factor** or **Lorentz term** is the factor by which time, length, and relativistic mass change for an object while that object is moving. The expression appears in several equations in special relativity, and it arises in derivations of the Lorentz transformations. The name originates from its earlier appearance in Lorentzian electrodynamics – named after the Dutch physicist Hendrik Lorentz.

In celestial mechanics the **specific relative angular momentum**
plays a pivotal role in the analysis of the two-body problem. One can show that it is a constant vector for a given orbit under ideal conditions. This essentially proves Kepler's second law.

In physics, **relativistic mechanics** refers to mechanics compatible with special relativity (SR) and general relativity (GR). It provides a non-quantum mechanical description of a system of particles, or of a fluid, in cases where the velocities of moving objects are comparable to the speed of light *c*. As a result, classical mechanics is extended correctly to particles traveling at high velocities and energies, and provides a consistent inclusion of electromagnetism with the mechanics of particles. This was not possible in Galilean relativity, where it would be permitted for particles and light to travel at *any* speed, including faster than light. The foundations of relativistic mechanics are the postulates of special relativity and general relativity. The unification of SR with quantum mechanics is relativistic quantum mechanics, while attempts for that of GR is quantum gravity, an unsolved problem in physics.

In experimental particle physics, **pseudorapidity**,
, is a commonly used spatial coordinate describing the angle of a particle relative to the beam axis. It is defined as

The **theoretical and experimental justification for the Schrödinger equation** motivates the discovery of the Schrödinger equation, the equation that describes the dynamics of nonrelativistic particles. The motivation uses photons, which are relativistic particles with dynamics determined by Maxwell's equations, as an analogue for all types of particles.

In physics, the **center-of-momentum frame** of a system is the unique inertial frame in which the total momentum of the system vanishes. The *center of momentum* of a system is not a location. Thus "center of momentum" means "center-of-momentum **frame**" and is a short form of this phrase.

In classical mechanics, **Euler's laws of motion** are equations of motion which extend Newton's laws of motion for point particle to rigid body motion. They were formulated by Leonhard Euler about 50 years after Isaac Newton formulated his laws.

**Lagrangian mechanics** is a reformulation of classical mechanics, introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in 1788.

The **Monte Carlo method for electron transport ** is a semiclassical Monte Carlo(MC) approach of modeling semiconductor transport. Assuming the carrier motion consists of free flights interrupted by scattering mechanisms, a computer is utilized to simulate the trajectories of particles as they move across the device under the influence of an electric field using classical mechanics. The scattering events and the duration of particle flight is determined through the use of random numbers.

**Tests of relativistic energy and momentum** are aimed at measuring the relativistic expressions for energy, momentum, and mass. According to special relativity, the properties of particles moving approximately at the speed of light significantly deviate from the predictions of Newtonian mechanics. For instance, the speed of light cannot be reached by massive particles.