Foundations & the classical crisis

energy quantum

An energy quantum is a single, indivisible packet of energy — the smallest amount that can be exchanged in a given process. The Latin word 'quantum' simply means 'how much', and it is from this idea of energy coming in countable lumps, rather than as a smooth continuous flow, that the entire field of quantum mechanics takes its name.

Classical physics had assumed energy could be subdivided forever, like water poured in any quantity you please. Planck's blackbody work suggested instead that, for a given frequency of light, energy is doled out only in whole packets each carrying E = hf. You can have one such packet or two, but never two and a half. The graininess is far too fine to notice in a kettle or a lamp, but it is decisive inside an atom.

This idea generalised far beyond light. The energy of an electron bound in an atom, the vibrations of a crystal, and the spin of a particle all turn out to come in discrete steps. 'Quantization' — the appearance of allowed values separated by gaps where no value is permitted — became the signature feature of the new physics, and the energy quantum was its first and founding example.

smallest exchangeable packet: E = hf (one quantum)

Energy changes hands in whole lumps of size hf, not in arbitrarily small trickles.

Not everything is quantized. A free particle, unbound by any well, can have any energy at all in a continuous range. Quantization of energy into discrete levels is a feature of confinement and bound states.

Also called
quantum of energyquantum能量子量子