Quantum interference with slits

Abstract

In the experiments considered here, we measure the y-component of momentum for a particle passing through a system of slits. The source-slit system is the preparation apparatus that determines the state vector. Recognizing that a system of slits is a positionmeasuring device allows us to ascertain that the state vector is a position state. Then, writing the state vector in momentum space provides a straightforward calculation for the probability amplitude and its corresponding probability function. Interference effects, if any, are inherent in the probability function We determine the statistical distribution of scattered particles for four different slit systems. The results are in agreement with the well-known interference patterns obtained in classical wave optics.

Event Based Interpretation of Schrödinger’s Equation for the Two-slit Experiment

“…Comparison of ρ(x, t) in Figs. 5 and 7 shows that the graphs are very similar, but there are The probability density ρ(x, t) for two symmetric slits with initial data a symmetric two-step step function (inset) with step centers at ±s = ±1.0, step widths 0.4 (a = 0.1), step height 1.0/ √ 8a = 1.0/ √ .8 as in (11), and corresponding envelope ρ + (x, t) + ρ − (x, t) formed from one-step step functions with initial data ψ 0+ (x), ψ 0− (x), centers at ±s = ±1.0, widths 0.4, and height 1.0/ √ 4a = 1.0/ √ .4. Secondary small amplitude waves are visible.…”

“…In the special case that the two slits are symmetric (that is, a 1 = a 2 = a), formula (6) simplifies (the case k = 0 is given in [10,11]):…”

“…In Fig. 9 we also graph ρ(x, t) for initial data a two-step step function as in (11), where the first phase wave pattern is established at t ≈ 2πsa, and is scale invariant for t > 2πsa. Fig.…”

Position Measurement-Induced Collapse: A Unified Quantum Description of Fraunhofer and Fresnel Diffractions

“…Among these works, the earliest one due to Marcella [3] proposes an expression to calculate the intensity of the diffracted beam using a reduced state ket of the particle. The collapse of state due to the process of measurement leads to this wave function, which is equivalently the projection of an initial state ket into the final one.…”

“…In the present work, we intend to study this issue and to suggest an alternative approach to that in [3]. In the first part, the general case of performing a measurement of position on a particle in one dimension is taken up.…”