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Physical Review A

Unified treatment of diffraction and 1f noise

Taher S. Sherif, Peter H. Handel

Published Jul 1, 1982• 36 citations
Publisher

Abstract

The two-particle wave function is used to study the diffraction pattern resulting from a double-slit experiment and to describe quantum $\frac{1}{f}$ noise from a beam of charged particles in vacuum. The density-matrix approach is also used to examine the case of $\frac{1}{f}$ noise resulting from a beam of scattered particles and to compare with the results we obtained with the two-particle wave-function method. The autocorrelation function was found analytically for the three cases mentioned above. The form of the autocorrelation function which we have obtained for $\frac{1}{f}$ noise is consistent with previous calculations of quantum $\frac{1}{f}$ noise, and is bilinear in the wave function, as required by the principles of quantum mechanics.

DOI
10.1103/physreva.26.596

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The two-particle wave function is used to study the diffraction pattern resulting from a double-slit experiment and to describe quantum 1f\frac{1}{f}f1​ noise from a beam of charged particles in vacuum. The density-matrix approach is also used to examine the case of 1f\frac{1}{f}f1​ noise resulting from a beam of scattered particles and to compare with the results we obtained with the two-particle wave-function method. The autocorrelation function was found analytically for the three cases mentioned above. The form of the autocorrelation function which we have obtained for 1f\frac{1}{f}f1​ noise is consistent with previous calculations of quantum 1f\frac{1}{f}f1​ noise, and is bilinear in the wave function, as required by the principles of quantum mechanics.
Abstract In this paper we apply the time-dependent quantum Monte Carlo (TDQMC) method to explore a modified single- and double-slit diffraction of matter waves. By using a simplified model of two electrons prepared in the ground state of an atom (molecule) and then suddenly released we are able to calculate the diffraction patterns in one spatial dimension in close correspondence with the numerically exact results. Through the Coulomb repulsion the one electron serves as an environment for the other, thus introducing decoherence in the quantum state which is easily quantified. It is demonstrated that the set of single particle wave functions yield by TDQMC can be used to directly construct a density matrix for that particle without tracing out the other constituents from the density matrix of the whole system. In this way it is possible to build explicitly time-dependent density matrices for different components of a complex quantum system straight within the TDQMC algorithm which may widen our understanding of quantum dynamics in many-body systems.
Numerical simulations of the double slit experiment with electrons, done by Al Rabeh, are repeated and improved. As well, the simulations go from moved Coulomb charges. These tests are extended with a proof of convergence for small time steps. Al Rabeh’s idea is fully confirmed: The pattern on the target comes from diffraction of charged particles, though it does not distinguish from interference pattern. In context with other results like that from Afshar, the wave-particle duality is disproved. The issue of photons is raised.
This paper provides a complete physical model associated with mathematical analysis and formulation that is based on Schrödinger equation and Feynman path integral. This model answers to single Photon (electron) double slit experiment with high degree of accuracy. It also gives a new method of analysis and formulation for Fresnel and Fraunhofer diffractions that are completely according to the Schrödinger equation and Feynman path concept. The results of these methods are precisely in agreement with the near field and far field diffraction experiments. In other words the new formulation in all above mentioned phenomena i.e. single photon (electron) double slit experiment, Fresnel and Fraunhofer diffractions are completely confirmed by lab experiments(measurements). Lab experiments mean common intensity and pattern experiments resulting from Fresnel (near field) diffraction, Fraunhofer (far field) diffraction and patterns resulting in single photon (electron) lab experiment. The resultant formulas are sketched and calculated by matlab program, the resultant graphs and values are compared with lab experiments in each section. This analysis substitutes wave function and probability density function concepts instead of interference of light beams emitted from infinitesimal pinholes or classical interpretation of near field diffraction and far field diffraction phenomena. The ultimate goal of this paper is to give a very accurate answer to the single particle double slit experiment and also to unify diffraction concept of classical optics in to quantum mechanics, deleting the traditional concept of phases in classical optics and substituting the concept of deflection of Feynman paths. The above mentioned analysis may be a glad tiding to a reliable method to unify classical optics in to quantum mechanics.
This paper provides a complete physical model associated with mathematical analysis and formulation that is based on Schrödinger equation and Feynman path integral. This model answers to single Photon (electron) double slit experiment with high degree of accuracy. It also gives a new method of analysis and formulation for Fresnel and Fraunhofer diffractions that are completely according to the Schrödinger equation and Feynman path concept. The results of these methods are precisely in agreement with the near field and far field diffraction experiments. In other words the new formulation in all above mentioned phenomena i.e. single photon (electron) double slit experiment, Fresnel and Fraunhofer diffractions are completely confirmed by lab experiments(measurements). Lab experiments mean common intensity and pattern experiments resulting from Fresnel (near field) diffraction, Fraunhofer (far field) diffraction and patterns resulting in single photon (electron) lab experiment. The resultant formulas are sketched and calculated by matlab program, the resultant graphs and values are compared with lab experiments in each section. This analysis substitutes wave function and probability density function concepts instead of interference of light beams emitted from infinitesimal pinholes or classical interpretation of near field diffraction and far field diffraction phenomena. The ultimate goal of this paper is to give a very accurate answer to the single particle double slit experiment and also to unify diffraction concept of classical optics in to quantum mechanics, deleting the traditional concept of phases in classical optics and substituting the concept of deflection of Feynman paths. The above mentioned analysis may be a glad tiding to a reliable method to unify classical optics in to quantum mechanics.
For various experiments to investigate quantum effects, matter-wave diffraction is an apparent example. Particle diffractions have been measured even at the large molecular level, such as the C 60 molecules. In order to describe the matter-wave diffraction of C 60 beam, we assume the initial wave functions behind a grating in form of the Fourier series with a Gaussian distribution function. By applying the Feynman path integral, the exact wave functions of the molecule diffraction in the near-field regime can be derived analytically. The obtained probability density distributions are corresponding to interference fringes as found in the Fresnel diffraction. The probability of finding C 60 molecules, behind the grating at the Talbot length, consistency with the mentioned experimental data of C 60 diffractions.
Abstract In this paper propagation of matter wave of particles is modeled using the Fourier optics approach. In first step the Schrödinger equation of quantum mechanics is used to find the wave function of the particle. In the second step Fourier optics is employed to model the diffraction of the wave function of the particle through single and double slits. The results of the calculations are presented as graphs of diffraction patterns. The results of the presented method are compared to the existing results in the literature (with different methods) to check the validity of the introduced model. It is shown that the Fourier optics approach is applicable to matter wave of particles in diffraction through slits.