Quantization

Quantization is the restriction of physical observables or allowed states to discrete values in a quantum description. It distinguishes quantum systems from classical models that permit continuous values.

Canonical quantization: A procedure that promotes classical coordinates and momenta to noncommuting quantum operators. It imposes quantum commutation relations on classical variables.
Quantum state: A mathematical description encoding the probabilities of outcomes for a quantum system. Quantization specifies which states and outcomes the description permits.
Atomic spectrum: The pattern of discrete wavelengths emitted or absorbed by atoms. Spectral lines reveal quantized energy differences between atomic states.
Classical mechanics: A theory describing motion through continuous variables such as position and momentum. Its continuous phase-space description is the starting point for many quantization procedures.
Black-body radiation: Electromagnetic radiation emitted by an ideal absorber in thermal equilibrium, with a spectrum determined by temperature. Its spectrum prompted Planck to introduce discrete energy exchanges.
Path integral quantization: A formulation of quantum theory that computes amplitudes by summing over possible histories weighted by action. It quantizes dynamics through a sum over histories rather than operator rules.
Observable: A measurable physical quantity represented by an operator in quantum mechanics. Quantization commonly appears as discrete possible measurement values of observables.
Quantum field theory: A framework describing particles as excitations of fields governed by quantum principles and special relativity. Field quantization is the basis of the modern theory of elementary particles.
Classical field theory: A theory in which physical fields vary continuously across space and time. Quantization replaces its classical fields with quantum operators or amplitudes.
Max Planck: A German theoretical physicist who introduced energy quantization in his account of black-body radiation. His 1900 proposal marks the beginning of quantum theory.

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