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...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.展开更多
The exact expressions of Gaussian-perturbation matrix elements in one- and two-mode Fock states are derived by virtue of the technique of integration within an ordered product of operators and the entangled state repr...The exact expressions of Gaussian-perturbation matrix elements in one- and two-mode Fock states are derived by virtue of the technique of integration within an ordered product of operators and the entangled state representation. It turns out that the matrix elements are just related to Gegenbauer polynomial and Hypergeometric function respectively. The 1st- and 2nd-order corrections to the energy levels and the 1st-order correction to wave functions of harmonic oscillator are deduced.展开更多
Some falsehoods of the so-called double-wave theory (DWT) are pointed out. The logic and the origin of the DWT, and three of the four fundamental hypotheses of DWT are criticized. It is expounded that the hypothesis o...Some falsehoods of the so-called double-wave theory (DWT) are pointed out. The logic and the origin of the DWT, and three of the four fundamental hypotheses of DWT are criticized. It is expounded that the hypothesis of two wave functions is unreasonable, the hypothesized Hamiltonian differs from the actually used Hamiltonian, and the hypothesized expression of measured values or mean values of mechanical quantities is wrong and does not express the measured values or mean values at all.展开更多
Parton physics,when formulated as light-front correlations,are difficult to study non-perturbatively,despite the promise of lightfront quantization.Recently an alternative approach to partons have been proposed by re-...Parton physics,when formulated as light-front correlations,are difficult to study non-perturbatively,despite the promise of lightfront quantization.Recently an alternative approach to partons have been proposed by re-visiting original Feynman picture of a hadron moving at asymptotically large momentum.Here I formulate the approach in the language of an effective field theory for a large hadron momentum P in lattice QCD,LaMET for short.I show that using this new effective theory,parton properties,including light-front parton wave functions,can be extracted from lattice observables in a systematic expansion of 1/P,much like that the parton distributions can be extracted from the hard scattering data at momentum scales of a few GeV.展开更多
文摘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.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10475056 and 10647133 and the Research Foundation of the Education Department of Jiangxi Province under Grant No. [2007]22
文摘The exact expressions of Gaussian-perturbation matrix elements in one- and two-mode Fock states are derived by virtue of the technique of integration within an ordered product of operators and the entangled state representation. It turns out that the matrix elements are just related to Gegenbauer polynomial and Hypergeometric function respectively. The 1st- and 2nd-order corrections to the energy levels and the 1st-order correction to wave functions of harmonic oscillator are deduced.
文摘Some falsehoods of the so-called double-wave theory (DWT) are pointed out. The logic and the origin of the DWT, and three of the four fundamental hypotheses of DWT are criticized. It is expounded that the hypothesis of two wave functions is unreasonable, the hypothesized Hamiltonian differs from the actually used Hamiltonian, and the hypothesized expression of measured values or mean values of mechanical quantities is wrong and does not express the measured values or mean values at all.
基金partially supported by the U.S.Department of Energy(Grant No.DE-FG02-93ER-40762)the Office of Science and Technology in Shanghai Municipal Government(Grant No.11DZ2260700)the National Natural Science Foundation of China(Grant No.11175114)
文摘Parton physics,when formulated as light-front correlations,are difficult to study non-perturbatively,despite the promise of lightfront quantization.Recently an alternative approach to partons have been proposed by re-visiting original Feynman picture of a hadron moving at asymptotically large momentum.Here I formulate the approach in the language of an effective field theory for a large hadron momentum P in lattice QCD,LaMET for short.I show that using this new effective theory,parton properties,including light-front parton wave functions,can be extracted from lattice observables in a systematic expansion of 1/P,much like that the parton distributions can be extracted from the hard scattering data at momentum scales of a few GeV.
