Quantum mechanics is the branch of physics relating to the very small.
It results in what may appear to be some extraordinary conclusions about the physical world. At the scale of atoms and electrons, many of the equations of classical mechanics, which describe how things move at common sizes and speeds, cease to be useful. In classical mechanics, objects exist in a specific place at a particular time. However, in quantum mechanics, objects instead exist in a haze of probability; they have a guaranteed chance of being at point A, another chance of being at point B, and so on.
Three revolutionary principles
Quantum mechanics (QM) developed over many decades, beginning as a set of controversial mathematical explanations of experiments that the math of classical mechanics could not explain. It started at the turn of the 20th century, around the same time that Albert Einstein published his theory of relativity, a separate mathematical revolution in physics that describes the motion of things at high speeds. Unlike relativity, however, the origins of QM cannot be attributed to any one scientist. Instead, multiple scientists contributed to a foundation of three revolutionary principles that gradually gained acceptance and experimental verification between 1900 and 1930. They are:
Quantized properties: Certain properties, such as position, speed, and color, can sometimes only occur in specific, set amounts, much like a dial that "clicks" from number to number. This challenged a fundamental assumption of classical mechanics, which said that such properties should exist on a smooth, continuous spectrum. To describe the idea that some features "clicked" like a dial with specific settings, scientists coined the word "quantized."
Particles of light: Light can sometimes behave as a particle. This was initially met with harsh criticism, as it ran contrary to 200 years of experiments showing that light behaved as a wave, much like ripples on the surface of a calm lake. Light behaves similarly in that it bounces off walls and bends around corners, and that the crests and troughs of the wave can add up or cancel out. Added wave crests result in brighter light, while waves that cancel out produce darkness. A light source can be thought of as a ball on a stick being rhythmically dipped in the center of a lake. The color emitted corresponds to the distance between the crests, which is determined by the speed of the ball's rhythm.
Waves of matter: Matter can also behave as a wave. This ran counter to the roughly 30 years of experiments showing that matter (such as electrons) exists as particles.
Quantized properties?
In 1900, German physicist Max Planck sought to explain the distribution of colors emitted over the spectrum in the glow of red-hot and white-hot objects, such as light-bulb filaments. When making physical sense of the equation he had derived to describe this distribution, Planck realized it implied that combinations of only certain colors (albeit a great number of them) were emitted, specifically those that were whole-number multiples of some base value. Somehow, the colors were quantized! This was unexpected because light was understood to act as a wave, meaning that values of color should be a continuous spectrum. What could be forbidding atoms from producing the colors between these whole-number multiples? This seemed so strange that Planck regarded quantization as nothing more than a mathematical trick. According to Helge Kragh in his 2000 article in Physics World magazine, "Max Planck, the Reluctant Revolutionary," "If a revolution occurred in physics in December 1900, nobody seemed to notice it. Planck was no exception …"
Planck's equation also contained a number that would later become very important to the future development of QM; today, it's known as "Planck's Constant."
Quantization helped to explain other mysteries of physics. In 1907, Einstein used Planck's hypothesis of quantization to explain why the temperature of a solid changed by different amounts if you put the same amount of heat into the material but changed the starting temperature.