We present a treatment of the double-slit interference of matter-waves represented by Gaussian wavepackets. The interference pattern is modelled with Green's function propagator which emphasizes the coordinate correlations and phases. We explore the connection between phases and position–momentum correlations in the intensity, visibility and predictability of the wavepacket interference. This formulation will indicate some aspects that can be useful for theoretical and experimental treatment of particle, atom or molecule interferometry and can be discussed in introductory quantum mechanics courses.
We present a treatment of the double-slit interference of matter-waves represented by Gaussian wavepackets. The interference pattern is modelled with Green's function propagator which emphasizes the coordinate correlations and phases. We explore the connection between phases and position–momentum correlations in the intensity, visibility and predictability of the wavepacket interference. This formulation will indicate some aspects that can be useful for theoretical and experimental treatment of particle, atom or molecule interferometry and can be discussed in introductory quantum mechanics courses.
The elements of reality coined by Einstein, Podolsky, and Rosen promoted a series of fundamental discussions involving the notion of quantum correlations and physical realism. The superposition principle applied in the double-slit experiment with matter waves highlights the need for a critical review of the adoption of physical realism in the quantum realm. In this work, we employ a measure of physical irrealism and consider an initial contractive state in the double-slit setup for which position and momentum variables of a single particle are initially correlated. We investigate how the behavior of the irrealism can help us to obtain information about the interference pattern, wavelike, and particlelike properties in the double-slit setup with matter waves. We find that there is a time of propagation that minimizes the irrealism, and around this point the state at the detection screen is squeezed in position and momentum in comparison with the standard Gaussian superposition. Interestingly, we show that the maximum visibility and the number of interference fringes are related to the minimum of the irrealism. Moreover, we demonstrate a monotonic relation between the irrealism and visibility around the time of minimum. Then, we argue how to use these results to indirectly measure the irrealism for position variable from the fringe visibility.
The double-slit experiment has stood for a century as the paradigmatic demonstration of quantum superposition: the standard interpretation holds that a particle passes through both slits simultaneously, existing in a superposition of two spatially separated states. This paper proposes a physically distinct alternative: the particle's matter wave — a real physical wave propagating through space in accordance with de Broglie's relation λ = h/p — passes through both slits, while the particle itself (matter) remains in an undetermined state until a constructive interference maximum is formed at the detection screen. The particle does not simultaneously occupy two locations; the wave does. This distinction eliminates the need for superposition as an ontological commitment while fully reproducing the observed interference pattern. We further show that the disappearance of the interference pattern upon which-path measurement is explained without invoking wavefunction collapse: the measurement interaction redirects the matter wave to a single-slit geometry, eliminating the two-wave interference condition. Three experimentally testable predictions distinguish this framework from the standard interpretation: (1) weak-measurement trajectory reconstruction should reveal single particle paths inconsistent with simultaneous two-slit passage; (2) diffraction fringe spacing should depend on the mass density of the slit material, because denser slit edges generate a steeper refractive-index gradient for the matter wave; (3) the fringe pattern should exhibit a density-dependent phase shift measurable with current matter-wave interferometry technology. This reinterpretation requires no new mathematical formalism — the Schrödinger equation and Born's rule are retained — but replaces the ontological claim of simultaneous multi-location existence with the physically consistent picture of matter-wave propagation through an undetermined-state particle.
Quantum correlations of observables for two particle states have demonstrated the nonlocal character of the quantum mechanics. However nonlocality can be exhibited even for noncommuting observables of a single particle system. In this paper we show nonlocality of position-momentum correlations of a single particle in the double-slit experiment modeled by an initially correlated Gaussian wavepacket. The positivity or negativity of the Wigner function for the state of the particle at the detection screen is related with the σxp covariances. A Bell's inequality is constructed from the Wigner function and it is violated for both the positive and negative cases. The case of positive Wigner function is the analogous of the original EPR state for a single particle.
This paper develops a phase-first reconstruction of quantum interference within standard quantum mechanics and wave optics. Its central idea is that interference patterns become conceptually clearer when the complex phase is treated as the organizing structure and probability or intensity density is treated as the visible statistical expression of that structure. The guiding principle is: the phase structures the pattern; the density renders it visible. The paper shows how this principle applies to single-slit diffraction, double-slit interference, Airy patterns, Fourier optics, Fresnel propagation, probability current, the Madelung representation, which-way marking, reduced coherence, and quantum eraser experiments. In each case, the observed density pattern is interpreted as the visible result of coherent phase relations among amplitudes. The reconstruction is strictly conservative. It does not modify quantum mechanics, the Born rule, unitary dynamics, or standard wave optics. It introduces no new postulates and makes no new empirical prediction. Its purpose is conceptual and pedagogical: to clarify the architecture of quantum interference by placing relative phase at the center of the analysis. This work is Part I of the series The Geometry of Phase. It establishes the phase-geometric foundation for later parts of the series, where the same perspective is extended to de Broglie matter waves, proper-time phase, relativistic action, and possible curvature-coupled phase extensions.
The double slit interference experiment has been famously described by Richard Feynman as containing the "only mystery of quantum mechanics". The history of quantum mechanics is intimately linked with the discovery of the dual nature of matter and radiation. While the double slit experiment for light is easily undertsood in terms of its wave nature, the very same experiment for particles like the electron is somewhat more difficult to comprehend. By the 1920s it was firmly established that electrons have a wave nature. However, for a very long time, most discussions pertaining to interference experiments for particles were merely gedanken experiments. It took almost six decades after the establishment of its wave nature to carry out a 'double slit interference' experiment for electrons. This set the stage for interference experiments with larger particles. In the last decade there has been spectacular progress in matter-wave interefernce experiments. Today, molecules with over a hundred atoms can be made to interfere. In the following we discuss some of these exciting developments which probe new regimes of Nature, bringing us closer to the heart of quantum mechanics and its hidden mysteries.
The Young’s single- and double-slit experiments are explained using six-component quantum and one-component quasi-classical photon wave functions in the coordinate representation, which are modeled by different mechanisms of photon diffraction on slits or simultaneous emission of two photons by (two) independent sources. This explanation is compared with the well-known statement about the interference of a particle with itself when passing through both slits simultaneously in the Young’s experiment on the basis of the postulated Feynman amplitudes. It is argued that these amplitudes cannot be wave functions, in the literal sense, describing some states of quantum particles. In all cases, under the assumption of the linear polarization of photons, a pronounced interference pattern has been obtained, which suggests that the coordinate wave function of a photon can explain the phenomena of the one- and two-photon interference. This conclusion, in turn, makes it possible to associate the coordinate wave function of a photon (two photons, in the entangled state) measured in some recent experiments with the quasi-classical wave function of a photon (two photons), although it does not take into account its (their) polarization properties.