Understanding single-slit experiments on the basis of Galton board experiments

2021 ◽  
Vol 34 (3) ◽  
pp. 265-267
Author(s):  
Chong Wang
Keyword(s):  
Normal Distribution ◽  
Probability Density ◽  
Least Action ◽  
Neighboring Particle ◽  
Large Particles ◽  
Pass Through ◽  
Particle Group ◽  
Slit Experiment

In a single-slit experiment conducted for microparticles, the well-aligned rough structure of the slit wall can be viewed as a Galton board. Thus, when microparticles pass through the single slit, both the particle probability density (PPD) and particle direction of motion have a normal distribution. Therefore, when the distance between the slit and the receiving film becomes large, particles with different directions of motion will separate into different particle groups. By the nature of a normal distribution, the PPD for any particle group should also be normal-distributed. Obviously, between any two neighboring particle groups, there should be a valley in the PPD and thus the particle groups are observed as discrete fringes. All phenomena observed in the single-slit experiment can be explained reasonably well from the above viewpoint. In particular, analysis shows that the PPD can be described by the square of the modulus of the average least action of particles at a given location.

Exploring the Phenomena of a Quantum Eraser in Young’s Double Slit Experiment

2020 ◽  
Author(s):  
Alexander Shaw ◽  
Trevor Vrckovnik ◽  
Billy Thorpe ◽  
Christian Sprang
Keyword(s):  
Interference Pattern ◽  
Quantitative Result ◽  
Bright Spot ◽  
Original Experiment ◽  
Quantum Eraser ◽  
Final Measurement ◽  
Pass Through ◽  
Double Slit Experiment ◽  
Slit Experiment ◽  
Double Slit

This experiment explores the quantum phenomenon known as the Quantum Eraser, using a variation of Young’s Double Slit experiment. Young’s Double Slit experiment demonstrates that light acts as a wave by creating an interference pattern when diffracted through two slits. If one measures which of the two slits the photons pass through, then the interference pattern is replaced by a single bright spot, as would be expected for particle-like behaviour. The “Quantum Eraser” eliminates the measurement on the photons, thereby reintroducing the interference pattern observed in Young’s original experiment. The experiment’s first stage saw Young’s Double Slit experiment recreated and an interference pattern was observed. Upon adding two orthogonally polarized filters, the photon’s path was measured, and the interference pattern was removed. By then adding a third filter which was polarized 45O relative to both other polarisers, the interference pattern was somewhat restored. For each experiment, the heights of the peaks in the interference patterns were compared to each other to examine the quality of the reproduced interference pattern based on the original double slit interference pattern. This comparison gave a quantitative result that demonstrated that the Quantum Eraser was able to restore the interference pattern to within 5 standard errors, thereby exemplifying the effect that changing the measurement conditions affects the final measurement.

Research Lifetime of Oil Film Bearing on High-Speed Wire Mill Based on Reliability Analysis

2011 ◽  
Vol 402 ◽  
pp. 358-361
Author(s):  
Shi Bo Jiang ◽  
Jie Liu ◽  
Jun Lin Ten
Keyword(s):  
Probability Density Function ◽  
Normal Distribution ◽  
Probability Density ◽  
Reliability Analysis ◽  
Density Function ◽  
High Speed ◽  
Statistical Data ◽  
Wire Mill ◽  
Oil Film ◽  
Wear Life

Based on the prerequisite that oil- film Bearing wear extent obey normal distribution，This paper come to reliability account formula through wear extent probability density function，deduce the wear life account formula of oil- film Bearing. based on detailed statistical data, calculate the lifetime of oil film bearing in High Speed Wire Rod finishing block, and forward the method how to raise the lifetime of oil- film Bearing.

scholarly journals Probability Density Functions for Prediction Using Normal and Exponential Distribution

2021 ◽  
pp. 40-52
Author(s):  
Kunio Takezawa
Keyword(s):  
Probability Density Function ◽  
Normal Distribution ◽  
Probability Density ◽  
Density Function ◽  
Exponential Distribution ◽  
Predictive Ability ◽  
Probability Density Functions ◽  
Density Functions ◽  
Specific Distribution ◽  
Using Data

When data are found to be realizations of a specific distribution, constructing the probability density function based on this distribution may not lead to the best prediction result. In this study, numerical simulations are conducted using data that follow a normal distribution, and we examine whether probability density functions that have shapes different from that of the normal distribution can yield larger log-likelihoods than the normal distribution in the light of future data. The results indicate that fitting realizations of the normal distribution to a different probability density function produces better results from the perspective of predictive ability. Similarly, a set of simulations using the exponential distribution shows that better predictions are obtained when the corresponding realizations are fitted to a probability density function that is slightly different from the exponential distribution. These observations demonstrate that when the form of the probability density function that generates the data is known, the use of another form of the probability density function may achieve more desirable results from the standpoint of prediction.

scholarly journals BOHMIAN TRAJECTORIES AND THE PATH INTEGRAL PARADIGM: COMPLEXIFIED LAGRANGIAN MECHANICS

2009 ◽  
Vol 19 (07) ◽  
pp. 2335-2346 ◽  
Author(s):  
VALERIY I. SBITNEV
Keyword(s):  
Probability Density ◽  
Path Integral ◽  
Balance Equation ◽  
Classical Mechanics ◽  
Nonlinear Function ◽  
Quantum Potential ◽  
Energy Term ◽  
Entropy Balance ◽  
Least Action ◽  
The Difference

David Bohm had shown that the Schrödinger equation, that is a "visiting card" of quantum mechanics, can be decomposed onto two equations for real functions — action and probability density. The first equation is the Hamilton–Jacobi (HJ) equation, a "visiting card" of classical mechanics, is modified by the Bohmian quantum potential. This potential is a nonlinear function of the probability density. And the second is the continuity equation. The latter can be transformed to the entropy balance equation. The Bohmian quantum potential is transformed into two Bohmian quantum correctors. The first corrector modifies the kinetic energy term of the HJ equation, and the second one modifies the potential energy term. The unification of the quantum HJ equation and the entropy balance equation gives a complexified HJ equation containing complex kinetic and potential terms. The imaginary parts of these terms have an order of smallness about the Planck constant. The Bohmian quantum corrector is an indispensable term modifying the Feynman's path integral by expanding coordinates and momenta to an imaginary sector. The difference between the Bohmian and Feynman's trajectories is that the former satisfies the principle of least action and they bifurcate on interfaces. The latter covers all possible paths from a source to a detector. They can split and annihilate.

scholarly journals Statistical analysis based on quaternion normal random variables

1985 ◽  
Vol 4 (3) ◽  
pp. 120-127 ◽  
Author(s):  
H. M. Rautenbach ◽  
J. J. J. Roux
Keyword(s):  
Statistical Analysis ◽  
Maximum Likelihood ◽  
Probability Density Function ◽  
Maximum Likelihood Estimation ◽  
Normal Distribution ◽  
Probability Density ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Unknown Parameters ◽  
Quaternion Case

The quaternion normal distribution is derived and a number of characteristics are highlighted. The maximum likelihood estimation procedure in the quaternion case is examined and the conclusion is reached that the estimation procedure is simplified if the unknown parameters of the associated real probability density function are estimated. The quaternion estimator is then obtained by regarding these estimators as the components of the quaternion estimator. By means of a example attention is given to a test criterium which can be used in the quaternion model.

Statistical Analysis of the Equivalent Noise Level

2015 ◽  
Vol 39 (2) ◽  
pp. 195-198 ◽  
Author(s):  
Wojciech Batko ◽  
Bartosz Przysucha
Keyword(s):  
Statistical Analysis ◽  
Probability Density Function ◽  
Normal Distribution ◽  
Probability Density ◽  
Noise Level ◽  
Sound Level ◽  
Uncertainty Calculation ◽  
Measurement Results ◽  
Interval Value

Abstract The authors focus their attention on the analysis of the probability density function of the equivalent noise level, in the context of a determination of the uncertainty of the obtained results in regard to the control of environmental acoustic hazards. In so doing, they discuss problems of correctness in the applicability of the classical normal distribution for the estimation of the expected interval value of the equivalent sound level. The authors also provide a set of procedures with respect to its derivation, based upon an assumption of the determined distribution of the measurement results. The obtained results then create the plane for the correct uncertainty calculation of the results of the determined controlled environmental acoustic hazard coefficient.

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