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# Quantum

## Definition of a quantum

Quantum physics is based on the discovery that physical properties on a microscopic level are not continuous, and instead take on discrete values.

Physical interactions appear continuous in daily life and most scientific contexts. When we consider extremely small quantities, we find that physical quantities (i.e. force, energy, fields) come in discrete packets.

A quantum is the smallest possible amount of any physical quantity. Any physical interaction between objects can be broken down into one or several (usually a very large number) of quanta.

A set of quanta is regarded in many situations as a group of particles (e.g. of energy, momentum, spin).

An electromagnetic wave is comprised of energy quanta transferred between two points in space.

## Photons

A photon is a quantum of electromagnetic radiation.

The energy of a photon $(E)$ can vary depending on the wavelength $\lambda$ (and therefore frequency $f$) of the electromagnetic radiation: $$E=hf=\frac{hc}{\lambda}$$

Recall that $f=v/\lambda\Rightarrow f=c/\lambda$ as electromagnetic waves travel at the speed of light (in a vacuum).

The total energy of a beam of radiation depends on the energy of an individual photon and the number of photons $N$ in the beam: $$E=Nhf$$

The Planck constant $(h)$ is a universal physical constant frequently used in quantum physics. $$h=6.63\times 10^{-34}\text{ J s}$$

$c=$ speed of light; $f=$ frequency; $h=$ Planck constant; $v=$velocity (of a wave); $\lambda=$ wavelength.

## Electron volt

Energies at the quantum level are often expressed in electron volts $(eV)$. One electron volt is defined as the charge of one electron $(1.6\times 10^{-19}\text{ C})$ multiplied by one volt: \begin{align*} E&=QV\\ &=1.6\times 10^{-19}\text{ C}\times 1\text{ V}\\ &=1.6\times 10^{-19}\text{ J}\\ &=1\text{ eV} \end{align*}

$E=$energy; $Q=$charge; $V=$potential.