An electromagnetic

Electromagnetism

Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...

 cavity is a cavity that acts as a container for electromagnetic field

Electromagnetic field

An electromagnetic field is a physical field produced by moving electrically charged objects. It affects the behavior of charged objects in the vicinity of the field. The electromagnetic field extends indefinitely throughout space and describes the electromagnetic interaction...

s such as photon

Photon

In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

s, in effect containing their wave function inside. The size of the cavity determines the maximum photon wave length that can be trapped. Additionally, it produces quantized energy level

Energy level

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

s for trapped charged particles like electrons and protons. The earth's magnetic field

Earth's magnetic field

Earth's magnetic field is the magnetic field that extends from the Earth's inner core to where it meets the solar wind, a stream of energetic particles emanating from the Sun...

 in effect places the earth

Earth

Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

 in an electromagnetic cavity.

Physical description of electromagnetic cavities

Electromagnetic cavities are represented by potential well

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 because it is captured in the local minimum of a potential well...

s, also called boxes, which can be of limited or unlimited depth V₀.

Quantum-mechanic boxes are described by the time-independent Schrödinger equation

Schrödinger equation

The Schrödinger equation was formulated in 1926 by Austrian physicist Erwin Schrödinger. Used in physics , it is an equation that describes how the quantum state of a physical system changes in time....

:
with the additional boundary conditions

• 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
• the wave function must be continuous
  Continuous function
  In mathematics, a continuous function is a function for which, intuitively, "small" changes in the input result in "small" changes in the output. Otherwise, a function is said to be "discontinuous". A continuous function with a continuous inverse function is called "bicontinuous".Continuity of...
  
  
• the derivative
  Derivative
  In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a...
  
   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 state

In physics, a bound state describes a system where a particle is subject to a potential such that the particle has a tendency to remain localised in one or more regions of space...

.

Applications of electromagnetic cavities

Electrons which are trapped in an electromagnetic cavity are in a bound state

Bound state

In physics, a bound state describes a system where a particle is subject to a potential such that the particle has a tendency to remain localised in one or more regions of space...

 and thus organise themselves as they do in a regular atom

Atom

The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...

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

Programmable matter

Programmable matter refers to matter which has the ability to change its physical properties in a programmable fashion, based upon user input or autonomous sensing...

 by varying the number of trapped electrons in those cavities.http://www.wired.com/wired/archive/9.10/atoms.html

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

Laser

A laser is a device that emits light through a process of optical amplification based on the stimulated emission of photons. The term "laser" originated as an acronym for Light Amplification by Stimulated Emission of Radiation...

 devices.

See also

• Cavity resonator
• Crab cavity
  Crab Cavity
  Crab cavities are a form of electromagnetic cavity used in particle accelerators to provide a transverse deflection to particle bunches. They can be used to provide rotation to a charged particle bunch by applying a time varying magnetic field...
  
  
• Schumann resonance
  Schumann resonance
  The Schumann resonances are a set of spectrum peaks in the extremely low frequency portion of the Earth's electromagnetic field spectrum...
  
  
• Optical cavity
  Optical cavity
  An optical cavity or optical resonator is an arrangement of mirrors that forms a standing wave cavity resonator for light waves. Optical cavities are a major component of lasers, surrounding the gain medium and providing feedback of the laser light. They are also used in optical parametric...
  
  
• Quantum dot
  Quantum dot
  A quantum dot is a portion of matter whose excitons are confined in all three spatial dimensions. Consequently, such materials have electronic properties intermediate between those of bulk semiconductors and those of discrete molecules. They were discovered at the beginning of the 1980s by Alexei...