Free particle

A free particle is an idealized particle with no external forces or interactions. Classically it moves at constant velocity; quantum mechanically it evolves under a free Hamiltonian.

Newton's first law: An object maintains rest or uniform straight-line motion unless acted on by a net external force. It gives the classical rule governing a particle when no net force acts.
Inertial frame: A reference frame in which force-free bodies move at constant velocity. Free-particle motion is defined relative to frames where Newton's first law holds.
Particle in a potential: A particle whose dynamics include a position-dependent potential energy. A potential adds interactions absent from the free-particle model.
Time-of-flight mass spectrometry: A method that identifies ions by measuring the time they take to travel a known distance. Ions travel through a force-free drift region whose flight time reveals their momentum-to-mass ratio.
Galileo Galilei: An Italian scientist whose work helped establish mathematical approaches to motion and inertia. His account of inertia helped prepare the classical idea of force-free motion.
Free-particle Hamiltonian: The quantum Hamiltonian for a particle whose energy is purely kinetic, typically \(\hat p^2/2m\). It encodes the free particle's energy and generates its quantum time evolution.
Momentum: A measure of motion, equal to mass times velocity in Newtonian mechanics. A free particle's momentum remains constant in the absence of forces.
Harmonic oscillator: A system whose restoring force is proportional to displacement from equilibrium. Its confining force contrasts with unbounded free motion.
Matter wave: A wave associated with a particle, with wavelength related to its momentum by de Broglie's relation. Free-particle wavefunctions make matter-wave behavior explicit.
Isaac Newton: An English mathematician and physicist who formulated the laws of classical mechanics. Newton's laws made constant-velocity motion the defining behavior of a force-free particle.

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