Transmission of Correlated Gaussian Packets Through a Delta-Potential

Dodonov, V. V.; Додонов, А. В.

doi:10.1007/s10946-014-9398-3

Cited by 23 publications

(4 citation statements)

References 35 publications

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“…In turn, we consider as the initial state the following correlated Gaussian state of transverse width that represents a position-momentum correlated Gaussian state. The initial correlation will be represented by the real parameter which can take values in the interval 44 , 45 . The parameter ensures that the initial state is correlated.…”

Section: Cross-wigner Function and Gouy Phase In Free Evolutionmentioning

confidence: 99%

Gouy phase and quantum interference with cross-Wigner functions for matter-waves

Marinho,

Dieguez,

Vieira

et al. 2024

Sci Rep

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The Gouy phase is essential for accurately describing various wave phenomena, ranging from classical electromagnetic waves to matter waves and quantum optics. In this work, we employ phase-space methods based on the cross-Wigner transformation to analyze spatial and temporal interference in the evolution of matter waves characterized initially by a correlated Gaussian wave packet. First, we consider the cross-Wigner of the initial wave function with its free evolution, and second for the evolution through a double-slit arrangement. Different from the wave function which acquires a global Gouy phase, we find that the cross-Wigner acquires a Gouy phase difference due to different evolution times. The results suggest that temporal like-Gouy phase difference is important for an accurate description of temporal interference. Furthermore, we propose a technique based on the Wigner function to reconstruct the cross-Wigner from the spatial intensity interference term in a double-slit experiment with matter waves.

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Section: Cross-wigner Function and Gouy Phase In Free Evolutionmentioning

confidence: 99%

Gouy phase and quantum interference with cross-Wigner functions for matter-waves

Marinho,

Dieguez,

Vieira

et al. 2024

Sci Rep

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show abstract

“…9.1.e. The theoretically expected pdf is found by applying the propagator (125) to the initial state 𝜓 0 shown in that section and is found as 𝜌(𝒙; 𝑡) = |𝜓(𝑥, 𝑡)| 2 , with [37] 𝜓(𝑥, 𝑡) = 𝜓 0 (𝑥, 𝑡) ⋅ 𝜓 1 (𝑥, 𝑡),…”

Section: Gaussian Wavementioning

confidence: 99%

A Local-Realistic Model of Quantum Mechanics Based on a Discrete Spacetime

Sciarretta¹

2017

Found Phys

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This paper presents a realistic, stochastic, and local model that reproduces nonrelativistic quantum mechanics (QM) results without using its mathematical formulation. The proposed model only uses integer-valued quantities and operations on probabilities, in particular assuming a discrete spacetime under the form of a Euclidean lattice. Individual (spinless) particle trajectories are described as random walks. Transition probabilities are simple functions of a few quantities that are either randomly associated to the particles during their preparation, or stored in the lattice nodes they visit during the walk. QM predictions are retrieved as probability distributions of similarly-prepared ensembles of particles. The scenarios considered to assess the model comprise of free particle, constant external force, harmonic oscillator, particle in a box, the Delta potential, particle on a ring, particle on a sphere and include quantization of energy levels and angular momentum.An event-based class of models have been recently proposed [25,26] that embody quantum behaviour into the constitutive models of the detectors and other devices, mostly using deterministic learning machines that generate events according to QM. This approach captures all of the features (R), (S), and (L). Interference, among other quantum phenomena, is not obtained as an intrinsic characteristic of the particles' trajectories but as a result of their interaction with the experimental apparatus.Other suggestions to make QM behaviour emerge from discrete time evolution [27] or vacuum fluctuations [2] were not pursued to the end, to our best knowledge.

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“…In Ref. [12] the evolution of Gaussian wave packet was studied in presence of the repulsive deltapotential barrier. For the initial packet localized far enough from the barrier, the transmission coefficient was determined as the probability of detecting a particle on the whole semi axis on the other side of the barrier.…”

Section: The Uncertainty Relationsmentioning

confidence: 99%

Harmonic Oscillator and Related States With Large Value of Uncertainty

Andreev¹

2017

RENSIT

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Transmission of Correlated Gaussian Packets Through a Delta-Potential

Cited by 23 publications

References 35 publications

Gouy phase and quantum interference with cross-Wigner functions for matter-waves

Gouy phase and quantum interference with cross-Wigner functions for matter-waves

A Local-Realistic Model of Quantum Mechanics Based on a Discrete Spacetime

Harmonic Oscillator and Related States With Large Value of Uncertainty

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