A measure of the capacity to do work, expressed in electronvolts for particle energies.Energy is a scalar quantity that represents the capacity of a physical system to perform work or produce change. It exists in many forms — kinetic, potential, thermal, electromagnetic, chemical, nuclear — and can be converted from one form to another, but never created or destroyed. In particle physics, energies are commonly expressed in electronvolts (eV), where 1 eV is the energy gained by an electron accelerated through a potential difference of one volt.
The modern concept of energy was formalized in the 19th century, with the law of conservation of energy established by Hermann von Helmholtz in 1847, building on earlier work by Joule, Mayer, and others.
Energy is conserved in isolated systems, meaning the total energy before and after any process remains constant. In mechanics, kinetic energy depends on mass and velocity squared; potential energy depends on position in a force field. In relativity, mass and energy are equivalent via E=mc², so even a stationary object has rest energy. In quantum mechanics, energy comes in discrete quanta for bound systems, such as electron orbitals in atoms.
Energy is the central quantity in all of physics and engineering — from power generation and propulsion to particle accelerators and nuclear reactors, where energy release and transfer are precisely calculated.
A single gram of matter, if fully converted to energy, would release about 90 terajoules — roughly the energy of a small nuclear bomb.
| E_n | variable | Energy of the nth level — energy joule |
| n | variable | Quantum number (non-negative integer) — quantum number |
| \hbar | constant | Reduced Planck constant — reduced planck constant = 1.054571817e-34 joule second |
| \omega | constant | Angular frequency of the oscillator — angular frequency radian per second |
| T | variable | tunneling probability — transmission probability |
| z1 | variable | left turning point of the barrier — position metre |
| z2 | variable | right turning point of the barrier — position metre |
| m | variable | mass of the tunneling particle — mass kilogram |
| V | variable | potential energy as a function of position — potential energy joule |
| E | variable | energy of the particle — energy joule |
| ħ | constant | fundamental quantum of action divided by 2π — reduced planck constant = 1.054571817e-34 joule second |
| ∫ | operator | sums the integrand over the interval — integral |
| √ | operator | takes the non-negative root — square root |
| exp | operator | raises e to the given power — exponential |
| E | variable | Energy of a photon — energy joule |
| f | variable | Frequency of the electromagnetic wave — frequency hertz |
| h | constant | Fundamental constant relating energy to frequency in quantum mechanics — planck constant = 6.62607015e-34 joule second |
| ⟨hν⟩ | variable | Average photon energy — energy joule |
| T | variable | Temperature of the blackbody — temperature kelvin |
| c | constant | A numerical factor that depends on the frequency integration limits and the specific definition of 'average' (e.g., over the full spectrum). — proportionality constant = 2.701 |
| k_B | constant | Fundamental constant converting temperature to energy scale — boltzmann constant = 1.380649e-23 joule per kelvin |
| ⟨ ⟩ | operator | Statistical average over the photon distribution — ensemble average |
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