摘要
Starting from the optical fractional Fourier transform (FFT) and using the technique of integration withinan ordered product of operators we establish a formalism of FFT for quantum mechanical wave functions. In doing so, theessence 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. Theyare generalized FFT. The relationship between the FFT and the rotated Wigner operator is studied by virtue of theWeyl ordered form of the Wigner operator.
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.
基金
国家自然科学基金，中国科学院院长基金，上海交通大学校科研和教改项目
