Two-Parameter Radon Transformation of the Wigner Operator and
Its Inverse
FAN Hong-Yi1,2, CHENG Hai-Ling2
1Department of Applied Physics, Shanghai Jiao Tong
University, Shanghai 200030
2Department of Materials Science and Engineering, University of Science and Technology of China, Hefei 230026
Two-Parameter Radon Transformation of the Wigner Operator and
Its Inverse
FAN Hong-Yi1,2;CHENG Hai-Ling2
1Department of Applied Physics, Shanghai Jiao Tong
University, Shanghai 200030
2Department of Materials Science and Engineering, University of Science and Technology of China, Hefei 230026
Abstract： Using the technique of integration within an ordered product of operators, we reveal that a new quantum mechanical representation |x,μ,v > exsit, the eigenvector of operator μQ+vP (linear combination of coordinate Q and momentum P) with eigenvalue x, which is inherent to the two-parameter(μ,v) Radon transformation of the Wigner operator. It turns out that the projection operator |x,μ,v > < x,μ,v | is just the Radon transformation of the Wigner operator. The inverse of operator Radon transformation is also derived which indicates tomography in operator version.
FAN Hong-Yi;CHENG Hai-Ling. Two-Parameter Radon Transformation of the Wigner Operator and
Its Inverse[J]. 中国物理快报, 2001, 18(7): 850-853.
FAN Hong-Yi, CHENG Hai-Ling. Two-Parameter Radon Transformation of the Wigner Operator and
Its Inverse. Chin. Phys. Lett., 2001, 18(7): 850-853.
2001, Vol. 18 
