Based on our previous paper (Commun.Theor.Phys.39 (2003) 417) we derive the convolution theoremof fractional Fourier transformation in the context of quantum mechanics,which seems a convenient and neat way.Generalizat...Based on our previous paper (Commun.Theor.Phys.39 (2003) 417) we derive the convolution theoremof fractional Fourier transformation in the context of quantum mechanics,which seems a convenient and neat way.Generalization of this method to the complex fractional Fourier transformation case is also possible.展开更多
Based on quantum mechanical representation and operator theory,this paper restates the two new convolutions of fractional Fourier transform(FrFT)by making full use of the conversion relationship between two mutual con...Based on quantum mechanical representation and operator theory,this paper restates the two new convolutions of fractional Fourier transform(FrFT)by making full use of the conversion relationship between two mutual conjugates:coordinate representation and momentum representation.This paper gives full play to the efficiency of Dirac notation and proves the convolutions of fractional Fourier transform from the perspective of quantum optics,a field that has been developing rapidly.These two new convolution methods have potential value in signal processing.展开更多
We show that the quantum-mechanical fundamental representations, say, the coordinate representation, the coherent state representation, the Fan-Klauder entangled state representation can be recast into s-ordering oper...We show that the quantum-mechanical fundamental representations, say, the coordinate representation, the coherent state representation, the Fan-Klauder entangled state representation can be recast into s-ordering operator expansion, which is elegant in form and has many applications in deriving new operator identities. This demonstrates that Dirac's symbolic method can be merged into Newton-Leibniz integration theory in a broad way.展开更多
基金National Natural Science Foundation of China under Grant No.10775097
文摘Based on our previous paper (Commun.Theor.Phys.39 (2003) 417) we derive the convolution theoremof fractional Fourier transformation in the context of quantum mechanics,which seems a convenient and neat way.Generalization of this method to the complex fractional Fourier transformation case is also possible.
基金National Natural Science Foundation of China(Grant Number:11304126)College Students' Innovation Training Program(Grant Number:202110299696X)。
文摘Based on quantum mechanical representation and operator theory,this paper restates the two new convolutions of fractional Fourier transform(FrFT)by making full use of the conversion relationship between two mutual conjugates:coordinate representation and momentum representation.This paper gives full play to the efficiency of Dirac notation and proves the convolutions of fractional Fourier transform from the perspective of quantum optics,a field that has been developing rapidly.These two new convolution methods have potential value in signal processing.
基金supported by the National Natural Science Foundation of China (Grant Nos.10775097 and 10874174)the Special Funds of the National Natural Science Foundation of China (Grant No.10947017/A05)+1 种基金the Higher School Fund of Outstanding Young Talent (Grant No.2010SQRL132)the Scientific Research Starting Foundation of Chizhou University (Grant No.2010RC036)
文摘We show that the quantum-mechanical fundamental representations, say, the coordinate representation, the coherent state representation, the Fan-Klauder entangled state representation can be recast into s-ordering operator expansion, which is elegant in form and has many applications in deriving new operator identities. This demonstrates that Dirac's symbolic method can be merged into Newton-Leibniz integration theory in a broad way.
