Atomic orbital

An atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons in an atom.

Quotes

 * The behavior of a specific electron in an atom can be described by a mathematical expression called a wave equation—the same type of expression used to describe the motion of waves in a fluid. The solution to a wave equation is called a wave function, or orbital, and is denoted by the Greek letter psi (ψ). … What do orbitals look like? There are four different kinds of orbitals, denoted s, p, d,and f,each with a different shape. … The orbitals in an atom are organized into different electron shells, centered around the nucleus and having successively larger size and energy.
 * John McMurry, Organic Chemistry 8th ed. (2012), Ch. 1 : Structure and Bonding


 * The simplified treatment presented here has as its basis the theory of quantum mechanics developed independently in the 1920s by Heisenberg, Schrödinger, and Dirac. In this theory, the movement of an electron around a nucleus is expressed in the form of equations that are very similar to those characteristic of waves. The solutions to these equations, called atomic orbitals, allow us to describe the probability of finding the electron in a certain region in space. The shapes of these regions  depend on the energy of the electron.
 * K. Peter C. Vollhardt, Neil E. Schore (2011) Organic chemistry : structure and function 6th ed. Chapter 1. Structure and Bonding in Organic Molecules


 * The motion of electrons around the nucleus is described by wave equations. Their solutions, atomic orbitals, can be symbolically represented as regions in space, with each point given a positive, negative, or zero (at the node) numerical value, the square of which represents the probability of finding the electron there. The Aufbau principle allows us to assign electronic configurations to all atoms.
 * K. Peter C. Vollhardt, Neil E. Schore (2011) Organic chemistry : structure and function 6th ed. Chapter 1. Structure and Bonding in Organic Molecules