Scattering amplitude is a fundamental concept in quantum mechanics and quantum field theory that describes the probability amplitude for a scattering process to occur. It quantifies how likely it is for incoming particles (or waves) to be scattered into a specific final state after interacting with each other. ### Key Points about Scattering Amplitude: 1. **Quantum Mechanics Framework**: In the context of quantum mechanics, the scattering amplitude is related to the wave function of the incoming and outgoing particles.
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A scattering amplitude is the complex coefficient relating a specified outgoing asymptotic component to a specified incident state. In three-dimensional short-range potential scattering with incident wave , the outgoing spherical part is .
In this convention has length units, and equal-speed elastic scattering gives . Other kinematics require flux or velocity factors. Contributions from indistinguishable alternatives are added as amplitudes before squaring, producing interference. An overall phase shared by the entire state is unobservable, while relative phases between partial waves affect angular distributions. A relativistically normalized matrix element uses different conventions and dimensions, so cross-section formulas cannot be transferred between amplitude definitions without their normalization factors.