Using squeezing transform in the context of quantum optics and based on the Fourier series expansion we rigorously derive a new Poisson sum formula. Application of this new formula to the representation transformation...Using squeezing transform in the context of quantum optics and based on the Fourier series expansion we rigorously derive a new Poisson sum formula. Application of this new formula to the representation transformation of kq-wave function for describing electrons in periodic lattice is demonstrated. In so doing, the transition matrix element of harmonic oscillator in kq representation is derived.展开更多
In this paper we set up quantum mechanical correspondence of the Poisson integral formula.We show that Poisson kernel function existing in the transformation between the continuum entangled state representation and it...In this paper we set up quantum mechanical correspondence of the Poisson integral formula.We show that Poisson kernel function existing in the transformation between the continuum entangled state representation and its induced state,i.e.the number-difference-correlated amplitude entangled state representation.展开更多
Polynomial splines have played an important role in image processing, medical imaging and wavelet theory. Exponential splines which are of more general concept have been recently investigated.We focus on cardinal expo...Polynomial splines have played an important role in image processing, medical imaging and wavelet theory. Exponential splines which are of more general concept have been recently investigated.We focus on cardinal exponential splines and develop a method to implement the exponential B-splines which form a Riesz basis of the space of cardinal exponential splines with finite energy.展开更多
基金Supported by the President Foundation of Chinese Academy of Sciencethe Specialized Research Fund for the Doctorial Progress of Higher Education in China under Grant No. 20070358009
文摘Using squeezing transform in the context of quantum optics and based on the Fourier series expansion we rigorously derive a new Poisson sum formula. Application of this new formula to the representation transformation of kq-wave function for describing electrons in periodic lattice is demonstrated. In so doing, the transition matrix element of harmonic oscillator in kq representation is derived.
基金Supported by the National Natural Science Foundation of China under Grant No.10874174 the Specialized Reserach Fund for The Doctoral Progress of Higher Education of China under Grant No.20070358009
文摘In this paper we set up quantum mechanical correspondence of the Poisson integral formula.We show that Poisson kernel function existing in the transformation between the continuum entangled state representation and its induced state,i.e.the number-difference-correlated amplitude entangled state representation.
文摘Polynomial splines have played an important role in image processing, medical imaging and wavelet theory. Exponential splines which are of more general concept have been recently investigated.We focus on cardinal exponential splines and develop a method to implement the exponential B-splines which form a Riesz basis of the space of cardinal exponential splines with finite energy.
