Quantum mechanics

Quantum mechanics is the fundamental physical <a href="/facts/Scientific_theory/moMsLrUn">theory</a> that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of <a href="/facts/Atom/69syB8dH">atoms</a>.: 1.1  It is the foundation of all quantum physics, which includes <a href="/facts/Quantum_chemistry/H9AXV0lx">quantum chemistry</a>, <a href="/facts/Quantum_field_theory/VoewsNJV">quantum field theory</a>, <a href="/facts/Quantum_technology/cp14mdhq">quantum technology</a>, and <a href="/facts/Quantum_information_science/JDuxpHp8">quantum information science</a>.
Quantum mechanics can describe many systems that <a href="/facts/Classical_physics/gGnINVPE">classical physics</a> cannot. Classical physics can describe many aspects of nature at an ordinary (<a href="/facts/Macroscopic/NLwPDtLe">macroscopic</a> and <a href="/facts/Microscopic_scale/EHg18xvy">(optical) microscopic</a>) scale, but is not sufficient for describing them at very small <a href="/facts/Submicroscopic/tICdS8xu">submicroscopic</a> (atomic and <a href="/facts/Subatomic/tMEzcTWQ">subatomic</a>) scales. Classical mechanics can be derived from quantum mechanics as an approximation that is valid at ordinary scales.
Quantum systems have <a href="/facts/Bound_state/NndW5JQl">bound</a> states that are <a href="/facts/Quantization_(physics)/fvs2Jwpn">quantized</a> to <a href="/facts/Discrete_mathematics/XdRUnzUL">discrete values</a> of <a href="/facts/Energy/wd8PrQM7">energy</a>, <a href="/facts/Momentum/TTkGv5eY">momentum</a>, <a href="/facts/Angular_momentum/7TuSVFxq">angular momentum</a>, and other quantities, in contrast to classical systems where these quantities can be measured continuously. Measurements of quantum systems show characteristics of both <a href="/facts/Particle/JHKr2w6h">particles</a> and <a href="/facts/Wave/3ANn7WXS">waves</a> (<a href="/facts/Wave%25E2%2580%2593particle_duality/Au3UlcwQ">wave–particle duality</a>), and there are limits to how accurately the value of a physical quantity can be predicted prior to its measurement, given a complete set of initial conditions (the <a href="/facts/Uncertainty_principle/UUSoSp4T">uncertainty principle</a>).
Quantum mechanics arose gradually from theories to explain observations that could not be reconciled with <a href="/facts/Classical_physics/gGnINVPE">classical physics</a>, such as <a href="/facts/Max_Planck/KKk0698y">Max Planck</a>'s solution in 1900 to the <a href="/facts/Black-body_radiation/f0fHghDy">black-body radiation</a> problem, and the correspondence between energy and frequency in <a href="/facts/Albert_Einstein/CNTet8qu">Albert Einstein</a>'s <a href="/facts/Annus_Mirabilis_papers/8LhL5hm7">1905 paper</a>, which explained the <a href="/facts/Photoelectric_effect/gIDcdm5U">photoelectric effect</a>. These early attempts to understand microscopic phenomena, now known as the "<a href="/facts/Old_quantum_theory/pXkHwvrh">old quantum theory</a>", led to the full development of quantum mechanics in the mid-1920s by <a href="/facts/Niels_Bohr/ydLPvQXT">Niels Bohr</a>, <a href="/facts/Erwin_Schr%25C3%25B6dinger/wCprepF2">Erwin Schrödinger</a>, <a href="/facts/Werner_Heisenberg/n4qzYvj4">Werner Heisenberg</a>, <a href="/facts/Max_Born/6VnUDWhA">Max Born</a>, <a href="/facts/Paul_Dirac/6bt5yRdk">Paul Dirac</a> and others. The modern theory is formulated in various <a href="/facts/Mathematical_formulations_of_quantum_mechanics/fRLw4sFU">specially developed mathematical formalisms</a>. In one of them, a mathematical entity called the <a href="/facts/Wave_function/KgM5ykjY">wave function</a> provides information, in the form of <a href="/facts/Probability_amplitude/ryPgJvs8">probability amplitudes</a>, about what measurements of a particle's energy, momentum, and other physical properties may yield.

Quantum mechanics open-in-new

Quantum mechanics