The phase space of finite systems (Q2724641)
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scientific article; zbMATH DE number 1618086
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The phase space of finite systems |
scientific article; zbMATH DE number 1618086 |
Statements
14 May 2002
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Newton equation
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Lie algebras
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optical waveguide
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Wigner function
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The phase space of finite systems (English)
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The Lie-Newton equation is defined as an analog of a Newton equation, which is also a harmonic oscillator equation, for a paraxial wave optics. The position, momentum, and Hamiltonian operators are defined and two distinct Lie algebras built. The difference operators representing the generators of \(\text{SU}(2)\) are built using these three operators. The solutions of the eigenvalue equation for the finite oscillator or waveguide are given in terms of Krawtchouk's polynomials, and called Krawtchouk functions. They are used to perform numerical simulations. The Wigner function is defined for a given function, and its physical meaning explained; then it is generalized for the 3-space. The Wigner function, being sesquilinear in two wavefields, serves for holographic encoding and decoding of finite signals.NEWLINENEWLINEFor the entire collection see [Zbl 0958.00039].
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