Quantum Energy Explained

Demystifying the science of quantum physics

TL;DR

In quantum physics, energy is discrete (chunky).

In classical physics, conforming to our intuitions, energy is continuous, meaning it can change smoothly. Imagine the differences between classical and quantum energy as a slide versus a staircase. Classically, changes in energy can be arbitrarily small. Whereas quantumly, energy only comes in discrete amounts — called quanta, which are also small but ultimately finite.

How did this all come about?

Let’s very briefly play back the tape.

1. Planck’s Quantization of Energy (1900)

In 1900, Max Planck introduced the idea that energy is quantized to solve the blackbody radiation problem. He proposed that energy is emitted or absorbed in discrete units, or quanta, and introduced Planck’s constant.

At the time, no one could derive the light spectrum emitted by hot objects. Source: E. Lummer and E. Pringsheim, ‘’1. Die Vertheilung der Energie im Spectrum des schwarzen Körpers und des blanken Platins; 2. Temperaturbestimmung fester glühender Körper,’’ Verhandlungen der Deutschen Physikalischen Gesellschaft 1 (1899), 215–35, on 217

This was a major theoretical step, but at the time, it was more of a mathematical fix than a fully understood physical principle.

2. Einstein and the Photoelectric Effect (1905)

In 1905, Albert Einstein applied the idea of energy quanta to light, proposing that light itself is made up of discrete packets of energy called photons, which he used to explain the photoelectric effect.

Millikan’s data for the cut-off voltage vs frequency. From, R. A. Millikan, Physical Review, vol. 7, pp 355–388, 1916. According to Einstein’s theory, the slope of this line should be equal to h/e, allowing Milkan to determine Planck’s constant.

This provided strong evidence for the quantization of light, helping to solidify the notion of discrete energy levels further, but this was still limited to electromagnetic radiation.

3. Bohr’s Model of the Atom (1913)

In 1913, Niels Bohr introduced his model of the atom, where electrons occupy discrete energy levels (or orbits) around the nucleus. Electrons could only move between these orbits by emitting or absorbing photons with energies corresponding to the difference between energy levels.