Quantum theory in simpler terms is the theoretical basis of physics that describes the nature and presence of matter and energy on the atomic and subatomic level. The nature of matter and energy on that level is sometimes referred to as Quantum physics or Quantum mechanics.

The most accurate clocks, atomic clocks use values of quantum theory to measure time. They track the specific radiation frequency required to make electrons bounce between energy levels.

There are a total of four quantum numbers:

The principal quantum figure – n

This quantum number appoints the principal electron shell. Because n is the most foreseeable distance of electrons from the nucleus, the bigger the number n is, the farther the electron is from the nucleus, the bigger the size of the orbital, and the bigger the atom is. n can only be any positive integer starting at 1, as n equal 1 appoints the first principle shell. The first principal shell is also named the ground state, or lowest energy state. This describes why n can not be zero or any negative integer, because there are no atoms with zero or a negative amount of energy levels/principal shells. When an electron gains energy or is an excited condition, it may leap to the second principle shell, where n equals 2. This is referred to as absorption because the electron is “absorbing” energy or photons. Electrons can also release energy as they leap to lower principle shells (This is called Emission) where n lessens by whole numbers. As the electron energy increases, so does the principal quantum figure, i.e. n = 3 meaning the third principal shell, n = 4 meaning the fourth principal shell, and etc.

The orbital angular momentum quantum figure – l

This figure determines the orbital shape and is therefore named the angular distribution. The number of angular nodes is equal to the value of the angular momentum quantum number l. Each value of l means a particular s, p, d, f subshell. The value of l is dependent on the principal quantum number n. The value of l however can be zero. It can also be a positive integer, but cannot be bigger than one less than principal quantum number (n-1).

The magnetic quantum figure – m_{l }

This number regulates the number of orbitals and their orientation inside a subshell. Its value also varies on the orbital angular momentum quantum number l. Given a certain l, m_{l }is an interval varying from –l–l to +l+l so it can be zero, a negative or positive integer._{ }_{ }

The electron spin quantum – m_{s}

This number, unlike the other three, does not rely on another quantum figure. It appoints the direction of the electron spin and may have a spin of +1/2, represented by ↑ or -1/2, represented by ↓. This means when m_{s} is positive the electron has an upward spin, which can always be referred to as “spin up”. When it’s negative the electron has a downward spin, so it would mean “spin down”. The importance of the electron spin quantum number is its determination of an atom’s ability to create a magnetic field or not.

According to Purdue University, quantum numbers come from the Bohr model, Schrödinger’s Hw = Ew wave equation, Hund’s rules and Hund-Mulliken orbital theory. It’s recommended to become familiarized with related physics and chemistry terms in order to understand the quantum figures that describe electrons in an atom.

Quantum mechanics developed over many decades, initially as a set of controversial mathematical explanations of experiments that the math of classical mechanics cannot describe. It started in the 20th century around when Einstein published his theory of relativity, which describes the motion of things at high speeds. The origination can only be accredited to a number of scientists who contributed to the grounds of three revolutionary principles that eventually earned acceptance and experimental verification between 1900 and 1930. They are the following:

Quantized properties: Particular properties, like position, speed and color, can at times only happen in specific, set amounts, much like a dial that “clicks” from figure to figure. This challenged a fundamental assumption of classical mechanics, which mention that such properties should exist on a smooth, continuous spectrum. Scientists described this process as “quantized” to describe concepts that some properties “clicked” like a dial with specific settings.

Particles of Light: Light can sometimes operate as a particle. This concept was initially criticized, as it was contradicting to 200 years of experiments showing that light behaved as a wave; like ripples on the surface of a calm lake. Light works similarly in that it jumps off walls and bends around corners, and that the crests and troughs of the wave can add up or cancel out. Added wave crests follow 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 radiating corresponds to the distance between the crests, which is settled by the speed of the ball’s rhythm. Einstein published a paper in 1905 known as, “Concerning an Heuristic Point of View Toward the Emission and Transformation of Light,” in where he foresees light traveling as a manner of “energy quanta” and not as a wave. Einstein explained this packet of energy could “be absorbed or generated only as a whole,” when an atom leaps between quantized vibration rates. This would also apply, as would be shown a few years later, when an electron leaps between quantized orbits. Under this representation, Einstein’s “energy quanta” includes the energy difference of the leap; when divided by Planck’s constant, that energy difference determined the color of light carried by those quanta.

For those who don’t know what Planck’s constant is, it’s simply denoted which is a physical constant that is the quantum of electromagnetic action which relates the energy carried by a photon to its frequency. The Planck constant is the basis for the definition of the kilogram.

Waves of Matter: Matter can also behave as a wave. This ran offset to the approximately 30 years of experiments showing that matter (i.e. electrons) live as particles. Since 1896 when electrons were discovered, proof that all matter existed in the form of particles was slowly building up. The presentation of light’s wave-particle duality made scientists articulate whether matter was restricted to acting only as particles. Maybe wave-particle duality could ring true for matter as well? The first scientist to make significant advancements with this reasoning was a French physicist called Louis de Broglie. In 1924, he used the equations of Einstein’s theory of special relativity to explain that particles can display wave-like components, and that waves can display particle-like components. In 1925, two scientists, working individually and using isolated lines of mathematical thinking, applied de Broglie’s reasoning to explain how electrons whizzed around in atoms (a phenomenon that was indescribable using equations of classical mechanics). In Germany, physicist Werner Heisenberg (collaborating with Pascual Jordan and Max Born) accomplished this by creating a similar theory called “wave mechanics”. In 1926, Schrödinger displayed that these two pathways were correspondent (though Swiss physicist Wolfgang Pauli sent an unpublished result to Jordan showing that matrix mechanics was more complete)