Kinetic energy in the context of "Hamiltonian operator"

Energy (from Ancient Greek ἐνέργεια (enérgeia) 'activity') is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light. Energy is a conserved quantity—the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The unit of measurement for energy in the International System of Units (SI) is the joule (J).

Forms of energy include the kinetic energy of a moving object, the potential energy stored by an object (for instance due to its position in a field), the elastic energy stored in a solid object, chemical energy associated with chemical reactions, the radiant energy carried by electromagnetic radiation, the internal energy contained within a thermodynamic system, and rest energy associated with an object's rest mass. These are not mutually exclusive.

Temperature quantitatively expresses the attribute of hotness or coldness. Temperature is measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making up a substance.

Thermometers are calibrated in various temperature scales that historically have relied on various reference points and thermometric substances for definition. The most common scales are the Celsius scale with the unit symbol °C (formerly called centigrade), the Fahrenheit scale (°F), and the Kelvin scale (K), with the third being used predominantly for scientific purposes. The kelvin is one of the seven base units in the International System of Units (SI).

Electricity generation is the process of generating electric power from sources of primary energy. For utilities in the electric power industry, it is the stage prior to its delivery (transmission, distribution, etc.) to end users or its storage, using for example, the pumped-storage method.

Consumable electricity is not freely available in nature, so it must be "produced", transforming other forms of energy to electricity. Production is carried out in power stations, also called "power plants". Electricity is most often generated at a power plant by electromechanical generators, primarily driven by heat engines fueled by combustion or nuclear fission, but also by other means such as the kinetic energy of flowing water and wind. Other energy sources include solar photovoltaics and geothermal power. There are exotic and speculative methods to recover energy, such as proposed fusion reactor designs which aim to directly extract energy from intense magnetic fields generated by fast-moving charged particles generated by the fusion reaction (see magnetohydrodynamics).

Hydropower (from Ancient Greek ὑδρο-, "water"), also known as water power or water energy, is the use of falling or fast-running water to produce electricity or to power machines. This is achieved by converting the gravitational potential or kinetic energy of a water source to produce power. Hydropower is a method of sustainable energy production. Hydropower is now used principally for hydroelectric power generation, and is also applied as one half of an energy storage system known as pumped-storage hydroelectricity.

Hydropower is an attractive alternative to fossil fuels as it does not directly produce carbon dioxide or other atmospheric pollutants and it provides a relatively consistent source of power. Nonetheless, it has economic, sociological, and environmental downsides and requires a sufficiently energetic source of water, such as a river or elevated lake. International institutions such as the World Bank view hydropower as a low-carbon means for economic development.

Cold is the presence of low temperature, especially in the atmosphere. In common usage, cold is often a subjective perception. A lower bound to temperature is absolute zero, defined as 0.00 K on the Kelvin scale, an absolute thermodynamic temperature scale. This corresponds to −273.15 °C on the Celsius scale, −459.67 °F on the Fahrenheit scale, and 0.00 °R on the Rankine scale.

Since temperature relates to the thermal energy held by an object or a sample of matter, which is the kinetic energy of the random motion of the particle constituents of matter, an object will have less thermal energy when it is colder and more when it is hotter. If it were possible to cool a system to absolute zero, all motion of the particles in a sample of matter would cease and they would be at complete rest in the classical sense. The object could be described as having zero thermal energy. Microscopically in the description of quantum mechanics, however, matter still has zero-point energy even at absolute zero, because of the uncertainty principle.

Deposition is the geological process in which sediments, soil and rocks are added to a landform or landmass. Wind, ice, water, and gravity transport previously weathered surface material, which, at the loss of enough kinetic energy in the fluid, is deposited, building up layers of sediment.

This occurs when the forces responsible for sediment transportation are no longer sufficient to overcome the forces of gravity and friction, creating a resistance to motion; this is known as the null-point hypothesis. Deposition can also refer to the buildup of sediment from organically derived matter or chemical processes. For example, chalk is made up partly of the microscopic calcium carbonate skeletons of marine plankton, the deposition of which induced chemical processes (diagenesis) to deposit further calcium carbonate. Similarly, the formation of coal begins with the deposition of organic material, mainly from plants, in anaerobic conditions.

The solar wind is a stream of charged particles released from the Sun's outermost atmospheric layer, the corona. This plasma mostly consists of electrons, protons and alpha particles with kinetic energy between 0.5 and 10 keV. The composition of the solar wind plasma also includes a mixture of particle species found in the solar plasma: trace amounts of heavy ions and atomic nuclei of elements such as carbon, nitrogen, oxygen, neon, magnesium, silicon, sulfur, and iron. There are also rarer traces of some other nuclei and isotopes such as phosphorus, titanium, chromium, and nickel's isotopes Ni, Ni, and Ni. Superimposed with the solar-wind plasma is the interplanetary magnetic field. The solar wind varies in density, temperature and speed over time and over solar latitude and longitude. Its particles can escape the Sun's gravity because of their high energy resulting from the high temperature of the corona, which in turn is a result of the coronal magnetic field. The boundary separating the corona from the solar wind is called the Alfvén surface.

At a distance of more than a few solar radii from the Sun, the solar wind reaches speeds of 250–750 km/s and is supersonic, meaning it moves faster than the speed of fast magnetosonic waves. The flow of the solar wind is no longer supersonic at the termination shock. Other related phenomena include the aurora (northern and southern lights), comet tails that always point away from the Sun, and geomagnetic storms that can change the direction of magnetic field lines.

Thermal radiation is electromagnetic radiation emitted by the thermal motion of particles in matter. All matter with a temperature greater than absolute zero emits thermal radiation. The emission of energy arises from a combination of electronic, molecular, and lattice oscillations in a material. Kinetic energy is converted to electromagnetism due to charge-acceleration or dipole oscillation. At room temperature, most of the emission is in the infrared (IR) spectrum, though above around 525 °C (977 °F) enough of it becomes visible for the matter to visibly glow. This visible glow is called incandescence. Thermal radiation is one of the fundamental mechanisms of heat transfer, along with conduction and convection.

The primary method by which the Sun transfers heat to the Earth is thermal radiation. This energy is partially absorbed and scattered in the atmosphere, the latter process being the reason why the sky is visibly blue. Much of the Sun's radiation transmits through the atmosphere to the surface where it is either absorbed or reflected.

Energy storage is the capture of energy produced at one time for use at a later time to reduce imbalances between energy demand and energy production. A device that stores energy is generally called an accumulator or battery. Energy comes in multiple forms including radiation, chemical, gravitational potential, electrical potential, electricity, elevated temperature, latent heat and kinetic. Energy storage involves converting energy from forms that are difficult to store to more conveniently or economically storable forms.

Some technologies provide short-term energy storage, while others can endure for much longer. Bulk energy storage is currently dominated by hydroelectric dams, both conventional as well as pumped. Grid energy storage is a collection of methods used for energy storage on a large scale within an electrical power grid.

A hammer is a tool, most often a hand tool, consisting of a weighted "head" fixed to a long handle that is swung to deliver an impact to a small area of an object. This can be, for example, to drive nails into wood, to shape metal (as with a forge), or to crush rock. Hammers are used for a wide range of driving, shaping, breaking and non-destructive striking applications. Traditional disciplines include carpentry, blacksmithing, warfare, and percussive musicianship (as with a gong).

Hammering is use of a hammer in its strike capacity, as opposed to prying with a secondary claw or grappling with a secondary hook. Carpentry and blacksmithing hammers are generally wielded from a stationary stance against a stationary target as gripped and propelled with one arm, in a lengthy downward planar arc—downward to add kinetic energy to the impact—pivoting mainly around the shoulder and elbow, with a small but brisk wrist rotation shortly before impact; for extreme impact, concurrent motions of the torso and knee can lower the shoulder joint during the swing to further increase the length of the swing arc (but this is tiring). War hammers are often wielded in non-vertical planes of motion, with a far greater share of energy input provided from the legs and hips, which can also include a lunging motion, especially against moving targets. Small mallets can be swung from the wrists in a smaller motion permitting a much higher cadence of repeated strikes. Use of hammers and heavy mallets for demolition must adapt the hammer stroke to the location and orientation of the target, which can necessitate a clubbing or golfing motion with a two-handed grip.