Quantum theory

Quantum theory is the body of physical theories describing matter and energy through quantized states and probabilistic rules. It accounts for phenomena that classical physics cannot, including atomic spectra and entanglement.

Wave function: A mathematical description of a quantum system that encodes probability amplitudes for possible measurement outcomes. It represents a system’s state and supplies the probabilities quantum theory predicts.
Hilbert space: A complete vector space with an inner product, used to represent quantum states and their relationships. Quantum states and measurement operators are formulated within this mathematical space.
Black-body radiation: Electromagnetic radiation emitted by an ideal absorber whose spectrum depends on temperature. Its spectrum exposed the failure of classical predictions at high frequencies.
Classical mechanics: The framework describing motion through deterministic laws such as Newton’s equations. It approximates quantum predictions for many large-scale systems but lacks their probabilistic structure.
Semiconductor: A material whose electrical conductivity lies between that of a conductor and an insulator and can be controlled. Quantum energy bands explain how semiconductor devices control electrical current.
Schrödinger equation: A differential equation governing how a quantum state changes over time. It specifies continuous state evolution between measurements in nonrelativistic quantum mechanics.
Observable: A physical quantity represented in quantum mechanics by a self-adjoint operator. Its possible measurement values correspond to the operator’s eigenvalues.
Max Planck: German physicist who introduced energy quantization to derive the black-body radiation spectrum. His 1900 proposal marks the beginning of quantum theory.
Copenhagen interpretation: A family of interpretations emphasizing quantum probabilities and the role of measurement outcomes. It offers a historically influential account of how quantum states relate to observations.
Laser: A device that amplifies light through stimulated emission, producing a coherent optical beam. Quantized atomic or material energy levels make stimulated emission possible.

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