# 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.

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.

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.