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Wave superposition: a motion of particle

Hyunhwan Choi

Published Jan 5, 2026• 0 citations
Publisher

Abstract

An attempt to explain the motion of particle is made in terms of a wave superposition. There is no localized superposition of waves that is supposed to be a single particle apart from other wave superposition, but there are a bunch of wave packets, which appears to be particle within a wave superposition that is made of individual waves around the space. There are countless number of waves that become a wave superposition, and the position of each wave packet is determined by the relative distance between packets, which is a superposition state. When a wave superposition interfere with a individual wave, this distance changes, and the position of each wave packet is fixed , which is called a measurement. With respect to the position of a particle, thus the particle is placed at the different position simultaneously in the superposition state. A change of the relative distance between wave packets appears to be a motion of particle, which is interpreted as a force acting on a particle. The photo-electric effect is explained in the same way, by which a superposition of charge waves interferes with the light wave, which increases the relative distance of wave packets in the atom, and it brings the outermost wave packet apart from the atom. The resistance in conductor is also understood by the wave interference with a superposition of charge waves residing in the conductor.

DOI
10.5281/zenodo.18151179

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An attempt to explain the motion of particle is made in terms of a wave superposition. There is no localized superposition of waves that is supposed to be a single particle apart from other wave superposition, but there are a bunch of wave packets, which appears to be particle within a wave superposition that is made of individual waves around the space. There are countless number of waves that become a wave superposition, and the position of each wave packet is determined by the relative distance between packets, which is a superposition state. When a wave superposition interfere with a individual wave, this distance changes, and the position of each wave packet is fixed , which is called a measurement. With respect to the position of a particle, thus the particle is placed at the different position simultaneously in the superposition state. A change of the relative distance between wave packets appears to be a motion of particle, which is interpreted as a force acting on a particle. The photo-electric effect is explained in the same way, by which a superposition of charge waves interferes with the light wave, which increases the relative distance of wave packets in the atom, and it brings the outermost wave packet apart from the atom. The resistance in conductor is also understood by the wave interference with a superposition of charge waves residing in the conductor.
A consistent description of the motion of a particle by wave propagation implies not only a geometrical equivalence between a trajectory and a ray but also a kinematical equivalence between the time rates at which the particle or wave is traversing its path. This may be tentatively achieved by using a wave configuration, known as a wave packet, represented as a continuous superposition of monochromatic waves. If the wave packet can be regarded as a point, having zero amplitude everywhere except in a very small region, its motion along a trajectory might be interpreted as the motion of a single particle. The representation of a particle in space and time by means of a highly localized wave packet is a basic assumption of wave mechanics. The behavior of the wave packet as a whole will account for experiments where particle-like properties are observed, whereas individual wavelength components of packet will appear in experiments which depend upon interference and diffraction effects.
The behaviour of localized quantum wave packet has lately become an object of much interest to forge a link between classical and quantum mechanics. Wave packet is often taken as the best approximation of quantum theory to a classical particle. If the wave packet is regarded as a point, with zero amplitude everywhere except in a very small region, then its motion can be interpreted as the motion of a single particle. The advent of short-pulsed lasers made it possible to produce and detect superposition of electron states for many physical systems. Such superposition leads to the formation of localized electron wave packets. The localized wave packet solution disperses or spreads in time, however, at a later time, it reforms and appears as its initial state. Revivals in quantum systems were first studied in the Jaynes–Cumming model, describing a two-level atom interacting with a resonant monochromatic field.
The operations of many detection devices are usually explained in terms of the ionization tracks produced by classical charged particles. A wave-mechanical analysis does not seem to be available. Mott [Proc. R. Soc. London Ser. A 126, 79 (1929)] has shown that an incident \ensuremath{\alpha} wave emitted by a radioactive nucleus would be scattered by atoms primarily in directions almost forward. However, these scattered waves would appear over the entire sensitive region of the detector. The mechanism that produces a collapse of the wave function to a single track is analyzed here. The incident \ensuremath{\alpha} wave is written as a superposition of minimum-sized packets. Since it is linear, the Schr\"odinger equation for the system including an observer can be solved for each packet individually. After the minimum packets interact with the electrons in the detector, they cannot be recombined to form a plane wave. However, they can be combined in groups to form larger coherent packets interacting with the detector to form tracks. The size and shape of each coherent packet is determined by the properties of the medium that is ionized to produce its track. The track from each packet is seen by the observer and is associated with a state of his memory, recording only one track. Each such packet replaces the particle in the usual explanation. These are the packets required to predict the quantum jumps seen in the scattering of laser light from an isolated atom as I have discussed [Phys. Rev. A 45, 4925 (1992)]. The relation of the probability distribution of these tracks to the wave function is explained.
In quantum mechanics the situation is different because the uncertainty principle does not allow us to know the initial positions and momenta of the particles with desired accuracy. The individual particle is described by a wave packet. Since the wave packet is localized and spreading with time, it is impossible to distinguish two identical particles as their wave functions always overlap at any point in space. Quantum theory describes any object at energies below its excitation threshold with four degrees of freedom. The wave functions of all the states of a given system of identical particles must have the same symmetry; otherwise, the wave function of a state formally a superposition of states of different symmetry would be neither symmetrical nor antisymmetrical. Hence, for a system of identical particles, at high energies and low concentration, probable number of particles per quantum state will be very small. Wave functions of the particles are well separated.
Abstract In this paper, we investigate mechanical motion of ultra-slow single atoms considering each atom is coherently coupled to a traveling-wave light. The main noise in this system is originated from Doppler broadening due to the continuous momentum distribution in atom wave packet. Here, it is proved that the Doppler broadening could be effectively suppressed in strong coupling regime. Under the coherent coupling, individual neutral atoms periodically walk in a definite direction. Direction of the motion depends on occupation of the atom in its two internal states related to the optical transition, since the atom would be affected by attractive or repulsive forces depending on the internal states. It is analogous to the electric force acting on negatively or positively charged particles. We explain them with spin–orbit coupling of atoms which is hidden in our Hamiltonian. These results have potential applications for the construction of future atomic devices.