S-matrix
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In physics, the '''S-matrix or scattering matrix''' is a matrix that relates the initial state and the final state of a physical system undergoing a scattering process. It is used in quantum mechanics, scattering theory and quantum field theory (QFT).
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Article
27 sectionsContents
- History
- Motivation
- Use
- In one-dimensional quantum mechanics
- Definition
- Unitary property
- Time-reversal symmetry
- Transfer matrix
- Finite square well
- Finite square barrier
- Transmission coefficient and reflection coefficient
- Optical theorem in one dimension
- Definition in quantum field theory
- Interaction picture
- In and out states
- From vacuum
- Heisenberg picture
- From free particle states
- In states expressed as out states
- ''S''-matrix
- Evolution operator ''U''
- Dyson series
- The not-''S''-matrix
- See also
- Remarks
- Notes
- References
In physics, the '''S-matrix or scattering matrix' is a matrix that relates the initial state and the final state of a physical system undergoing a scattering process. It is used in quantum mechanics, scattering theory and quantum field theory (QFT).
More formally, in the context of QFT, the S-matrix is defined as the unitary matrix connecting sets of asymptotically free particle states (the in-states and the out-states) in the Hilbert space of physical states: a multi-particle state is said to be free (or non-interacting) if it transforms under Lorentz transformations as a tensor product, or direct product in physics parlance, of one-particle states as prescribed by equation below. Asymptotically free then means that the state has this appearance in either the distant past or the distant future.