Quantum mechanics (QM) is a set of scientific principles describing the known behavior of energy and matter that predominate at the atomic and subatomic scales. The name derives from the observation that some physical quantities—such as the energy of an electron—can be changed only by set amounts, or quanta, rather than being capable of varying by any amount. The wave–particle duality of energy and matter at the atomic scale provides a unified view of the behavior of particles such as photons and electrons. Photons are the quanta of light, and have energy values proportional to their frequency via the Planck constant. An electron bound in an atomic orbital has quantized values of angular momentum and energy. The unbound electron does not exhibit quantized energy levels, but is associated with a quantum mechanical wavelength, as are all massive particles. The full significance of the Planck constant is expressed in physics through the abstract mathematical notion of action.

The mathematical formulation of quantum mechanics is abstract and its implications are often non-intuitive. The centerpiece of this mathematical system is the wavefunction. The wavefunction is a mathematical function of time and space that can provide information about the position and momentum of a particle, but only as probabilities, as dictated by the constraints imposed by the uncertainty principle. Mathematical manipulations of the wavefunction usually involve the bra-ket notation, which requires an understanding of complex numbers and linear functionals. Many of the results of QM can only be expressed mathematically and do not have models that are as easy to visualize as those of classical mechanics. For instance, the ground state in quantum mechanical model is a non-zero energy state that is the lowest permitted energy state of a system, rather than a more traditional system that is thought of as simple being at rest with zero kinetic energy.