具有二次哈密顿量和多变量Hermite多项式的多模量子系统的层析成像
Tomography of multimode quantum systems with quadratic Hamiltonians and multivariable Hermite polynomials
摘要：
综述了具有位置和动量二次型多模非定常哈密顿算符的系统。讨论了二次系统的Fock态和Gauss态的层析概率分布。Fock态的层析图用多变量Hermite多项式表示。利用这些明显的物理关系，得到了多变量厄米多项式的一些新公式，并给出了振子和电荷在电磁场中运动的例子。
英文摘要：
The 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. Using the obvious physical relations some new formulas for multivariable Hermite polynomials are found. Examples of oscillator and charge moving in electromagnetic field are presented.
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