Quantum mechanics (QM), also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic scales. In advanced topics of QM, some of these behaviors are macroscopic and only emerge at very low or very high energies or temperatures. The name, coined by Max Planck, derives from the observation that some physical quantities can be changed only by discrete amounts, or quanta, as multiples of the Planck constant, rather than being capable of varying continuously or by any arbitrary amount. For example, the angular momentum, or more generally the action, of an electron bound into an atom or molecule is quantized. An electron bound in an atomic orbital has quantized values of angular momentum while an unbound electron does not exhibit quantized energy levels. In the context of QM, the wave–particle duality of energy and matter and the uncertainty principle provide a unified view of the behavior of photons, electrons and other atomic-scale objects.
The mathematical formulations of quantum mechanics are abstract and the implications are often non-intuitive in terms of classic physics. The centerpiece of the mathematical system is the wavefunction. The wavefunction is a mathematical function that can provide information about the probability amplitude of position and momentum of a particle. Mathematical manipulations of the wavefunction usually involve the bra-ket notation, which requires an understanding of complex numbers and linear functionals. The wavefunction emphasizes the object as a quantum harmonic oscillator and the mathematics is akin to that of acoustics, resonance. Many of the results of QM do not have models that are easily visualized in terms of classical mechanics; for instance, the ground state in the 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 simply being at rest with zero kinetic energy.
