A quantum experiment consists of a preparation procedure followed by the measurement of a specified observable. In the experiments considered here, the y -component of momentum is measured after a particle passes through a system of slits. The source–slit system is the preparation apparatus that determines the initial state |ψ⟩. Recognizing that a system of slits is a position-measuring device allows us to determine |ψ⟩. Then, a straightforward calculation gives P ( p y ) = |⟨ p y |ψ⟩| 2 the probability that a particle will pass through a system of slits with momentum p y = p sin θ. Interference effects are inherent in this probability function. We perform the calculation for four different slit systems. The method is suitable for an upper level course in quantum mechanics.
A quantum experiment consists of a preparation procedure followed by the measurement of a specified observable. In the experiments considered here, the y -component of momentum is measured after a particle passes through a system of slits. The source–slit system is the preparation apparatus that determines the initial state |ψ⟩. Recognizing that a system of slits is a position-measuring device allows us to determine |ψ⟩. Then, a straightforward calculation gives P ( p y ) = |⟨ p y |ψ⟩| 2 the probability that a particle will pass through a system of slits with momentum p y = p sin θ. Interference effects are inherent in this probability function. We perform the calculation for four different slit systems. The method is suitable for an upper level course in quantum mechanics.
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 position-measuring 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.
This work proposes a novel variation of the double-slit experiment in which two different types of quantum particles — for example, electrons and photons — pass simultaneously through a shared double-slit apparatus. The primary objective is to test the hypothesis that the act of measurement may not only collapse the wave function of the observed particle, but could also influence the interference pattern of an unmeasured, co-propagating particle of a different type. In the proposed configuration, photons and electrons are emitted in synchrony and directed through the same set of slits. Immediately after the slits, a path-detecting measurement apparatus is applied only to one type of particle (e.g., photons), while the interference pattern of the other type (e.g., electrons) is recorded on a distant screen. The experiment is designed to explore whether the destruction of coherence through measurement is strictly local, or whether it can propagate to other particles through a shared medium, entangled fields, or an unknown interaction. If the unmeasured particle continues to display interference, this would support the locality of measurement effects. Conversely, if interference vanishes for both, it could indicate a more global or field-level decoherence process. This investigation aims to contribute new insights into the nature of quantum measurement, the role of observation, and the interdependence of coherent systems involving distinct particle species.
Particles which pass through slits can be classified as three types: Type (I): particles which only pass through slit A and arrive in the screen position x meaning the probability of passing through slit A is 1; Type (II): particles which only pass through slit B and arrive in the screen position x meaning the probability of passing through slit B is 1; Type (III): the probability of passing through slit A is c1(0 < c1 < 1), and the probability of passing through slit B is c2 (0 < c2 < 1). When only slit A is open, the particles in the neighborhood of x(x is interference position) consist of Type (I) particles. In this case, the particle’s density in position x is |ψ1|, where ψ1 is the state function of particles which pass through slit A. When only slit B is open, the particles in the neighborhood of x consist of Type (II) particles. In this case, the particle’s density in position x is |ψ2|, where ψ2 is the state function of particles which pass through slit B. When A and B open simultaneously, Type (III) particles should be taken into account: if they pass through slit A, their particle density dedication to position x is c1|ψ1|; if they pass through slit B, their particle density dedication to position x is c2|ψ2|. The average dedication in the neighborhood of x should be the geometric average of c1|ψ1| and c2|ψ2| , that is: √ c1|ψ1| c2|ψ2| = c1c2|ψ1||ψ2|.
The double slit experiment provides a classic example of both interference and the effect of observation in quantum physics. When particles are sent individually through a pair of slits, a wave-like interference pattern develops, but no such interference is found when one observes which "path" the particles take. We present a model of interference, dephasing, and measurement-induced decoherence in a one-dimensional version of the double-slit experiment. Using this model, we demonstrate how the loss of interference in the system is correlated with the information gain by the measuring apparatus/observer. In doing so, we give a modern account of measurement in this paradigmatic example of quantum physics that is accessible to students taking quantum mechanics at the graduate or senior undergraduate levels.
Summary form only given. We say that the quantum observables "position" and "momentum" are "complementary" because the precise knowledge of the position (momentum) implies that all possible outcomes of measuring the momentum (position) are equally probable. In two-slit experiments, the common understanding is that the position-momentum uncertainty relation makes it impossible to determine which slit the photon (or electron) passes through without at the same time disturbing the object enough to destroy the interference pattern. In 1982, Scully et al. suggested a way around this position-momentum uncertainty obstacle and proposed a quantum eraser to obtain which-path or particle-like information without scattering or otherwise introducing large uncontrolled phase factors to disturb the interference. Since 1982, quantum has been claimed in several experiments; however, the original proposed ideas have not been fully demonstrated. We demonstrate them here.
In classical physics, interactions appear to be of the form of cause and effect, as in Newton’s second law is: F = dp/dt. The force F governs the interaction and dp/dt is the effect. In quantum mechanics, there is a probability for an impulse hit interaction by a particle given by exp(ipx) within a wavelength region of size hbar/p. As a result, instead of an interaction occurring within dx->0, the particle itself dictates an interaction region of the size hbar/p. Consequently, in a 2-slit interaction, the slits should be about a wavelength hbar/p apart. In classical physics, an interaction occurs within the interaction region (dx->0), but in the 2-slit case the interaction region includes the space from the first slit to the second, so to ask: What is happening as the particle interacts within this region? means that a particle can pass through one slit and inteact with the other, or it can interact with the slit through which it passes. The interaction region is the smallest region in which the interaction occurs (as if it were a black box). The particle physically passes through one slit or the other, but interacts either way with both slits probabilisitcally because otherwise the interaction region would only be one slit or the other contradicting the probabilistic range hbar/p of interaction. As a result, a two-slit calculation is really a calculation of an interaction within an hbar/p region including both slits. This interaction is probabilistic due to the exp(ipx) interaction hit nature of the particle and so it is the particle which dictates the interaction to a large degree. The fact that the particle must pass through one slit or the other, together with a probabilistic interaction over the hbar/p region means that two key notions are at work, one being the physical location of the particle (passing through one slit or the other) which governs how the probabilistic interaction (due to the particle) operates. In particular, one draws two parallel rays, one from the center of each slit towards a fixed point on a screen far away. The interaction is based on the exp(ipx) probabilistic interaction of the particle and the separation of the two slits because the particle interacts with both as it passes through only one. In other words, reality is not simply based on what one can measure during an interaction. The fact that one does measure through which slit the particle passes does not mean that the positions of the slits cannot stil helpl lead to determinate statements such as zero particles arrive at certain x points on the screen. The slit separation is part of the physical reality of the problem. (Note: there is also diffraction from the two edges of each slit, i.e. diffraction, which follows the same ideas and so one has a combination of diffraction from each slit together with interference.) As a result, we suggest that one consider the entire region from one slit to the other as a quantum interaction region similar to the dx->0 used in Newtonian mechanics. Quantum mechanics then provides a probabilistic, not deterministic, descripition of possible interactions and their probability weights, unlike the cause (force) and effect (deterministic change in p of the particle) of Newtonian mechanics. The exp(ipx), hbar/p gradation form of probability, allows for probabilities to add or subtract at different x points. The walls of the 2-slit apparatus are linked with probabilistic momentum angle changing, with each angle having the same probability (uniform distribution), but otherwise much of the interaction is dictated by the particle, unlike in Netwonian mechanics. For a V(x) = Sum over i Vk exp(ikx), both exp(ipx) and exp(ikx) are one a similar footing.