Quantum Physics Glossary: Key Terms and Definitions

Quantum physics describes the behavior of matter and energy at atomic and subatomic scales, where classical Newtonian mechanics fails to accurately predict experimental outcomes. This glossary covers the foundational terms, theoretical constructs, and measurement concepts that appear throughout quantum mechanics, quantum field theory, and quantum information science. Precision in terminology is essential because many quantum concepts carry meanings that differ substantially from their colloquial uses, and misapplication of terms produces compounding errors in technical reasoning. The Quantum Physics Authority index provides broader navigational context for how these concepts connect across the discipline.

Definition and scope

Quantum physics, as formally structured by bodies including the American Physical Society (APS) and codified in the curricula of institutions such as the Massachusetts Institute of Technology OpenCourseWare physics sequence, encompasses the theoretical and experimental study of physical systems whose behavior is governed by quantization — the principle that certain physical quantities, such as energy, angular momentum, and electric charge, exist only in discrete packets rather than continuous values.

The glossary scope covers four primary conceptual clusters:

1. Foundational principles — quantization, wave-particle duality, the uncertainty principle, and superposition
2. State and measurement formalism — quantum states, wavefunctions, operators, eigenvalues, and observables
3. Entanglement and nonlocality — Bell states, EPR correlations, and decoherence
4. Applied quantum concepts — quantum tunneling, spin, and quantum numbers

The following definitions are drawn from standard references including the National Institute of Standards and Technology (NIST) physical constants database (NIST CODATA) and publicly available syllabi from federal research institution physics programs.

Core term definitions

Quantum — The smallest discrete unit of a physical quantity that can exist independently. Planck's constant, h = 6.62607015 × 10⁻³⁴ joule-seconds (NIST CODATA 2018), defines the scale at which quantum effects govern energy exchange.

Wavefunction (ψ) — A mathematical function that encodes the probability amplitude of all possible states of a quantum system. The square of the wavefunction's absolute value, |ψ|², gives the probability density of finding a particle at a specific location upon measurement. The wavefunction is a solution to the Schrödinger equation.

Superposition — A quantum system existing in a linear combination of two or more eigenstates simultaneously until a measurement collapses it to a single eigenstate. Superposition is not analogous to classical uncertainty; the system genuinely occupies multiple states, a distinction confirmed by interference experiments.

Heisenberg Uncertainty Principle — A fundamental limit stating that the standard deviations of position (σₓ) and momentum (σₚ) of a particle satisfy σₓ · σₚ ≥ ℏ/2, where ℏ is the reduced Planck constant. This is not an artifact of measurement imprecision but an intrinsic property of quantum systems, as established by Werner Heisenberg's 1927 paper.

Entanglement — A correlation between two or more quantum particles such that the quantum state of each cannot be described independently of the others, regardless of the spatial separation between them. John Bell's 1964 theorem, published in Physics (Vol. 1), established inequalities whose violation by experimental results rules out local hidden-variable explanations.

Decoherence — The process by which a quantum system loses its superposition character through interaction with its environment, causing quantum interference terms to vanish and classical probabilistic behavior to emerge. Decoherence timescales in superconducting qubits are typically measured in microseconds.

Quantum Tunneling — The phenomenon whereby a quantum particle penetrates a potential energy barrier that classical mechanics would prohibit it from crossing. Tunneling probability depends exponentially on barrier width and height and is governed by the transmission coefficient derived from the Schrödinger equation.

Spin — An intrinsic form of angular momentum carried by quantum particles, characterized by a spin quantum number (s). Electrons carry spin-1/2, meaning their spin can be measured as +ℏ/2 or −ℏ/2 along any axis. Photons carry spin-1.

Eigenvalue and Eigenstate — When a quantum operator acts on a wavefunction and returns that wavefunction multiplied by a scalar, that scalar is the eigenvalue and the wavefunction is the eigenstate. Measurement outcomes in quantum mechanics correspond exclusively to eigenvalues of the relevant observable operator.

Qubit — The fundamental unit of quantum information, analogous to the classical bit but capable of superposition. A qubit state is described as α|0⟩ + β|1⟩, where |α|² + |β|² = 1. The National Quantum Initiative Act (Public Law 115-368) formally established federal investment priorities around qubit-based quantum computing.

How it works

The mathematical structure of quantum mechanics rests on linear algebra applied to complex vector spaces called Hilbert spaces. Physical states are vectors in a Hilbert space; physical observables are represented by Hermitian operators acting on those vectors.

The time evolution of a quantum state follows the Schrödinger equation:

iℏ ∂ψ/∂t = Ĥψ

where Ĥ is the Hamiltonian operator representing total energy. This equation is deterministic — the wavefunction evolves predictably between measurements. The indeterminacy enters only at the moment of measurement, when the wavefunction collapses to a specific eigenstate with probability |ψ|².

The distinction between quantum mechanics and quantum field theory (QFT) is definitional, not merely one of scale:

The Standard Model of particle physics, maintained as a reference by CERN and described in detail through Fermilab's public physics resources, is a quantum field theory incorporating three of the four fundamental forces.

Common scenarios

Quantum physics terminology appears in 3 distinct applied contexts, each demanding terminological precision:

1. Quantum computing — Terms such as qubit, superposition, entanglement, and gate fidelity have precise technical meanings. A quantum gate is a unitary operator acting on qubits; "quantum supremacy" (sometimes called quantum advantage) refers to a specific computational benchmark, not a general capability claim. Google's 2019 result, published in Nature (Vol. 574), demonstrated a specific 53-qubit processor completing a sampling task in 200 seconds.

2. Quantum cryptography and post-quantum cryptography — These are distinct fields. Quantum key distribution (QKD) uses quantum mechanical properties to distribute cryptographic keys. Post-quantum cryptography uses classical algorithms resistant to quantum attacks. NIST published its first 3 post-quantum cryptographic standards in 2024 under FIPS 203, FIPS 204, and FIPS 205 (NIST Post-Quantum Cryptography).

3. Spectroscopy and atomic physics — Quantum numbers (principal n, angular momentum ℓ, magnetic mℓ, spin ms) classify electron states within atoms. These appear in spectroscopic notation standardized by the International Union of Pure and Applied Chemistry (IUPAC) in its published recommendations.

Decision boundaries

Certain term pairs in quantum physics are frequently conflated; the boundaries between them are definitional:

Superposition vs. mixed state — A superposition (pure state) is a coherent linear combination of basis states described by a single wavefunction. A mixed state is a statistical ensemble of pure states, described by a density matrix, and represents classical ignorance rather than quantum coherence. The density matrix formalism, standard in quantum information theory as described in Nielsen and Chuang's Quantum Computation and Quantum Information (Cambridge University Press), is necessary to represent mixed states correctly.

Entanglement vs. correlation — Classical correlations arise from shared prior information (hidden variables). Quantum entanglement produces correlations that violate Bell inequalities, confirmed in loophole-free experiments including Hensen et al. (2015) published in Nature (Vol. 526). Not all quantum correlations constitute entanglement; separable mixed states can display classical correlations.

Wave-particle duality vs. observer effect — Wave-particle duality refers to the dual description required for quantum objects — neither purely classical wave nor purely classical particle. The observer effect refers to the disturbance introduced by measurement. These are related but not equivalent: duality is an intrinsic property; the observer effect is a consequence of physical interaction during measurement.

Quantum tunneling vs. barrier penetration in classical waves — Classical evanescent waves in optics exhibit superficially similar barrier penetration but arise from Maxwell's equations, not quantum mechanics. True quantum tunneling applies to massive particles and is governed by the Schrödinger equation with no classical analogue.

For researchers navigating the scope of quantum physics within broader scientific research frameworks, the key dimensions and scopes of scientific research page provides structural context on how subfield boundaries are established across physics and adjacent disciplines.

References

• NIST CODATA
• NIST Post-Quantum Cryptography