Fractional Fourier Transformation for Quantum Mechanical Wave Functions Studied by Virtue of IWOP Technique
Fractional Fourier Transformation for Quantum Mechanical Wave Functions Studied by Virtue of IWOP Technique
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DOI：
10.1088/0253-6102/39/4/417
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发表时间：
2003-04
影响因子：
3.1
通讯作者：
Hong-Yi Fan;Fan Yue
中科院分区：
文献类型：
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作者：
Hong-Yi Fan;Fan Yue
从光学分数傅里叶变换（FFT）出发，利用算符序积内积分技术，建立了量子力学波函数的FFT形式。这样可以更清楚地看到FFT的本质，也可以更直接、更简洁地导出某些波函数的FFT。我们还指出，不同的FFT积分核对应于不同的量子力学表示。它们是广义FFT。利用Wigner算子的Weyl序形式研究了FFT与旋转Wigner算子之间的关系。
Starting from the optical fractional Fourier transform (FFT) and using the technique of integration within an ordered product of operators we establish a formalism of FFT for quantum mechanical wave functions. In doing so, the essence of FFT can be seen more clearly, and the FFT of some wave functions can be derived more directly and concisely. We also point out that different FFT integral kernels correspond to different quantum mechanical representations. They are generalized FFT. The relationship between the FFT and the rotated Wigner operator is studied by virtue of the Weyl ordered form of the Wigner operator.