An electromagnetic cavity is a

cavity Cavity may refer to: Biology and healthcare *Body cavity, a fluid-filled space in many animals where organs typically develop **Gastrovascular cavity, the primary organ of digestion and circulation in cnidarians and flatworms *Dental cavity or too ...

that acts as a container for

electromagnetic field An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical c ...

s such as

photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always ...

s, in effect containing their

wave function A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements mad ...

inside. The size of the cavity determines the maximum photon wavelength that can be trapped. Additionally, it produces quantized

energy level A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical particles, which can have any amount of energy. The te ...

s for trapped charged particles like

electrons The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no ...

and

protons A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...

. The

earth's magnetic field Earth's magnetic field, also known as the geomagnetic field, is the magnetic field that extends from Earth's interior out into space, where it interacts with the solar wind, a stream of charged particles emanating from the Sun. The magnetic f ...

in effect places the

earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...

in an electromagnetic cavity.

Physical description of electromagnetic cavities

Electromagnetic cavities are represented by

potential well A potential well is the region surrounding a local minimum of potential energy. Energy captured in a potential well is unable to convert to another type of energy (kinetic energy in the case of a gravitational potential well) because it is captur ...

s, also called ''boxes'', which can be of limited or unlimited depth V₀. Quantum-mechanic boxes are described by the time-independent

Schrödinger equation The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of the ...

: :

\psi(\mathbf) = E \psi (\mathbf),

with the additional

boundary condition In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. A solution to a boundary value problem is a solution to th ...

s * the wave function is confined to the box (infinite deep potential well) or approaches zero as the distance from the wall increases to infinity, thus

normalisable A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements mad ...

* the wave function must be

continuous Continuity or continuous may refer to: Mathematics * Continuity (mathematics), the opposing concept to discreteness; common examples include ** Continuous probability distribution or random variable in probability and statistics ** Continuous ...

* the

derivative In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. F ...

of the wave function must be continuous which leads to real solutions for the wave functions if the net energy of the particle is negative., i.e. if the particle is in a

bound state Bound or bounds may refer to: Mathematics * Bound variable * Upper and lower bounds, observed limits of mathematical functions Physics * Bound state, a particle that has a tendency to remain localized in one or more regions of space Geography *B ...

Applications of electromagnetic cavities

Electrons which are trapped in an electromagnetic cavity are in a

and thus organise themselves as they do in a regular

atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, and ...

, thus expressing chemical-like behaviour. Several researchers have proposed to develop

programmable matter Programmable matter is matter which has the ability to change its physical properties (shape, density, moduli, conductivity, optical properties, etc.) in a programmable fashion, based upon user input or autonomous sensing. Programmable matter is ...

by varying the number of trapped electrons in those cavities."Ultimate Alchemy"
''Wired'', Issue 9.10, Oct 2001. Retrieved 23 October 2012 The discrete energy levels of electromagnetic cavities are exploited to produce photons of desired frequencies and thus are essential for nano- or submicrometre-scale

laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The fir ...

devices.

References

Electromagnetism {{electromagnetism-stub

Physical description of electromagnetic cavities

Applications of electromagnetic cavities

See also

References