Correspondence principle

The correspondence principle requires quantum predictions to approach classical physics in the appropriate large-scale limit, such as for systems with large quantum numbers.

Ehrenfest theorem: A quantum-mechanical result relating the time evolution of expectation values to classical equations of motion. It shows how average quantum positions and momenta can follow Newtonian dynamics.
Niels Bohr: A Danish physicist who developed an influential model of the atom and helped establish quantum theory. Bohr formulated the principle while developing his account of atomic spectra.
Planck constant: The fundamental constant setting the scale of quantum action. Classical behavior often emerges when relevant actions greatly exceed its scale.
Bohr correspondence principle: Bohr's specific rule connecting quantum transition frequencies with classical frequencies at large quantum numbers. It is the historically narrower version tied to atomic transitions.
WKB approximation: A semiclassical method that approximates wavefunctions when their phase varies rapidly compared with their amplitude. Its classical limit connects quantum phase to particle trajectories.
Old quantum theory: Early quantum models that imposed quantization on classical ideas before modern quantum mechanics. The principle first guided this transitional framework.
Quantum number: A discrete label specifying an allowed value of a quantum observable or state. Large quantum numbers are a classic route to correspondence.
Quantum-classical transition: The emergence of classical descriptions from quantum systems under appropriate conditions. This broader problem includes correspondence but also asks how classical behavior appears.
Hamilton–Jacobi equation: A formulation of classical mechanics in which the action satisfies a first-order partial differential equation. The Schrödinger equation reduces to this equation in the semiclassical limit.
Bohr model: A model of the atom in which electrons occupy quantized circular orbits around the nucleus. Its spectral predictions approach classical orbital behavior at high quantum numbers.

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