Quantum Mechanics Glossary

A theorem proving that no local hidden variable theory can reproduce all predictions of quantum mechanics. Experimental violations of Bell inequalities confirm the non-local character of entanglement.

The postulate that the probability of a measurement outcome equals the squared magnitude $|c_i|^2$ of the corresponding probability amplitude in the wave function.

A particle with integer spin (0, 1, 2, etc.) that does not obey the Pauli exclusion principle. Examples include photons, gluons, and the Higgs boson.

The operation $[A, B] = AB - BA$ for two operators. Non-zero commutators indicate incompatible observables that cannot be simultaneously measured with arbitrary precision.

The standard interpretation of quantum mechanics holding that the wave function represents knowledge of a system and collapses upon measurement to a definite eigenstate.

The wavelength associated with a moving particle, given by $\lambda = h/p$, demonstrating the wave nature of matter.

The process by which quantum superpositions are lost through interaction with the environment, effectively producing classical-like behavior without invoking wave function collapse.

A quantum state that, when acted upon by an operator, yields the same state multiplied by a scalar (the eigenvalue). Measurement of an observable always yields one of its eigenvalues.

The scalar value obtained when an operator acts on its eigenstate. In quantum mechanics, eigenvalues of Hermitian operators represent possible measurement outcomes.

A quantum correlation between two or more particles such that the state of one cannot be fully described without reference to the others, regardless of spatial separation.

A particle with half-integer spin ($1/2, 3/2$, etc.) that obeys the Pauli exclusion principle. Examples include electrons, protons, and neutrons.

The operator corresponding to the total energy of a quantum system, used in the Schrodinger equation to determine time evolution.

A linear operator equal to its conjugate transpose, guaranteeing real eigenvalues. All observable quantities in quantum mechanics are represented by Hermitian operators.

A complete vector space with an inner product that provides the mathematical framework for quantum mechanics. Quantum states are vectors in this space.

An interpretation proposing that all possible measurement outcomes are realized in separate branching universes, eliminating the need for wave function collapse.

The quantum of the electromagnetic field, a massless spin-1 boson that carries electromagnetic force and has energy $E = hf$.

The fundamental constant $h = 6.626 \times 10^{-34}$ J·s that sets the scale of quantum phenomena and relates photon energy to frequency via $E = hf$.

A region where the potential energy exceeds a particle's total energy, classically forbidding passage. In quantum mechanics, particles can tunnel through such barriers with non-zero probability.

A model system with equally spaced energy levels $E_n = (n + \frac{1}{2})\hbar\omega$, fundamental to many areas of quantum physics including quantum field theory and molecular vibrations.

A discrete value that labels the quantum state of a particle. For atomic electrons, the four quantum numbers are principal ($n$), angular momentum ($l$), magnetic ($m_l$), and spin ($m_s$).

The phenomenon by which a particle traverses a potential energy barrier that it does not have sufficient classical energy to surmount, with probability decreasing exponentially with barrier width.

An intrinsic angular momentum of elementary particles with no classical analog. Electrons are spin-$1/2$ fermions and can have spin projections of $+1/2$ or $-1/2$.

The principle that a quantum system can exist in a linear combination of multiple states simultaneously until a measurement is performed.

A complex-valued function ($\psi$) that fully describes the quantum state of a system; its squared magnitude $|\psi|^2$ gives the probability density of measurement outcomes.

The minimum energy a quantum system possesses even in its ground state, arising from the uncertainty principle. A quantum harmonic oscillator has ground-state energy $\frac{1}{2}\hbar\omega$.