Abstract
Systems with multimode nonstationary Hamiltonians (quadratic in position and momentum operators) are reviewed. The tomographic probability distributions (tomograms) for the Fock states and Gaussian states of the quadratic systems are discussed. The tomograms for the Fock states are expressed in terms of multivariable Hermite polynomials. In view of the obvious physical relations, some new formulas for multivariable Hermite polynomials are found. Examples of a driven parametric oscillator and a charged particle moving in the electromagnetic field are presented.
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Man'ko, V.I., Sharapov, V.A. & Shchukin, E.V. Tomography of Multimode Quantum Systems with Quadratic Hamiltonians and Multivariable Hermite Polynomials. Journal of Russian Laser Research 22, 410–436 (2001). https://doi.org/10.1023/A:1012841404159
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DOI: https://doi.org/10.1023/A:1012841404159