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Feynman path integral
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Sum over all histories gives amplitudes.
The amplitude to go from A to B is the sum over all paths of e^{iS/ħ}. Classical paths arise where the action is stationary and phases add.
Describes the double slit as all paths through both slits.
Equivalent to Schrödinger's equation.
In more detail
The Feynman path integral sums over all possible paths of a particle, each weighted by a phase given by the action. Classical motion emerges where the phases add constructively.
Real-world uses
- Path integrals are used in quantum field theory calculations.
- They provide an alternative formulation of quantum mechanics.
- Theoretical physicists use Feynman's path integral to calculate scattering amplitudes and quantum corrections.
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Frequently asked questions
Does the particle take every path?
In the sum, yes, and the paths interfere to give the observed outcomes.
Why does classical motion appear?
Because paths near the classical one add constructively, while others cancel.
Does a particle really take every path?
The path integral is a way of computing amplitudes by summing over all paths, which is a powerful mathematical tool.
Related topics in Quantum Mechanics
Blackbody and Planck's law · Quantum statistics of light · Quantum field theory intro · Quantum electrodynamics · Casimir effect · Quantum Hall effect