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Quantum Reports
Special Issues
100 Years of Quantum Mechanics
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100 Years of Quantum Mechanics

A special issue of Quantum Reports (ISSN 2624-960X).

Deadline for manuscript submissions: 31 October 2025 | Viewed by 8743

Special Issue Editors

Prof. Dr. Viktor Dodonov

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Guest Editor
Instituto de Física e Centro Internacional de Física, Universidade de Brasília, Caixa Postal 04455, Brasília 70910-900, DF, Brazil
Interests: quantum physics; cavity electrodynamics; quantum closed and open systems with time-dependent parameters; uncertainty relations in quantum mechanics; nonclassical states of light in quantum optics
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Margarita A. Man’ko

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Guest Editor
Lebedev Physical Institute, Russian Academy of Sciences, Leninskii Prospect 53, Moscow 119991, Russia
Interests: quantum phase transition; quantum evolutions; quantum mechanics
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Salomon S. Mizrahi

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Guest Editor
Physics Department, Federal University of São Carlos, Via Washington Luiz km 235, São Carlos 13565, SP, Brazil
Interests: quantum information; atom-radiation interaction; measurement theory; photocounting; quantum computing
Prof. Dr. Luis L. Sánchez-Soto

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Guest Editor
Departamento de Óptica, Facultad de Fisica, Universidad Complutense, 28040 Madrid, Spain
Interests: quantum optics; quantum information; polarization; tomography; discrete quantum systems; phase-space method
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Soon, all physicists will celebrate 100 years of one of the most beautiful parts of physics, quantum mechanics. It was mainly developed during the years 1925–1927 in the works of such great scientists as Heisenberg, Born, Pauli, Dirac, Schrödinger, Landau, von Neumann, Bohr, and many others. Remember that the famous PhD thesis “Recherches sur la théorie des Quanta” was defended by Louis De Broglie in November 1924. It is remarkable that this area of physics, despite its honorary age, is still healthy and developing!

This can be easily seen in the topics of interest for the suggested Special Issue:

  • Uncertainty relations;
  • Quantum mechanics in phase spaces;
  • Quantum tomography;
  • Dynamics of open quantum systems in the presence of dissipation and decoherence;
  • Dynamics of quantum entanglement;
  • Quantum–classical transitions;
  • Quantum control of evolution;
  • Dynamical quantum invariants;
  • New exact and approximate solutions in quantum mechanics;
  • Path integral methods in quantum mechanics;
  • Non-Hermitian quantum mechanics;
  • Non-linear generalizations of quantum mechanics;
  • Quantum mechanics in finite-dimensional Hilbert spaces;
  • History of quantum mechanics;
  • Interpretations of quantum mechanics;
  • Tests of quantum mechanics.

Prof. Dr. Viktor Dodonov
Prof. Dr. Margarita A. Man’ko
Prof. Dr. Salomon S. Mizrahi
Prof. Dr. Luis L. Sánchez-Soto
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Quantum Reports is an international peer-reviewed open access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • quantum mechanics
  • quantum entanglement
  • quantum system
  • Schrödinger equation
  • quantum control

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (7 papers)

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Research

20 pages, 503 KiB  
Article
Probability Representation of Quantum States: Tomographic Representation in Standard Potentials and Peres–Horodecki Criterion for Probabilities
by Julio A. López-Saldívar, Margarita A. Man’ko and Vladimir I. Man’ko
Quantum Rep. 2025, 7(2), 22; https://doi.org/10.3390/quantum7020022 - 24 Apr 2025
Viewed by 87
Abstract
In connection with the International Year of Quantum Science and Technology, a review of joint works of the Lebedev Institute and the Mexican research group at UNAM is presented, especially related to solving the old problem of the state description, not only by [...] Read more.
In connection with the International Year of Quantum Science and Technology, a review of joint works of the Lebedev Institute and the Mexican research group at UNAM is presented, especially related to solving the old problem of the state description, not only by wave functions but also by conventional probability distributions analogous to quasiprobability distributions, like the Wigner function. Also, explicit expressions of tomographic representations describing the quantum states of particles moving in known potential wells are obtained and briefly discussed. In particular, we present the examples of the tomographic distributions for the free evolution, finite and infinite potential wells, and the Morse potential. Additional to this, an extension of the Peres–Horodecki separability criteria for momentum probability distributions is presented in the case of bipartite, asymmetrical, real states. Full article
(This article belongs to the Special Issue 100 Years of Quantum Mechanics)
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10 pages, 2400 KiB  
Article
Superoperator Approach to the Lindbladian Dynamics of a Mirror-Field System
by Marco A. García-Márquez and Héctor M. Moya-Cessa
Quantum Rep. 2025, 7(2), 15; https://doi.org/10.3390/quantum7020015 - 24 Mar 2025
Viewed by 200
Abstract
We use superoperator techniques to solve the master equation for the interaction between a single-mode quantized field and a single mechanical mode of a moving mirror, which is coupled to a zero-temperature reservoir that damps its amplitude. The solution we provide allows for [...] Read more.
We use superoperator techniques to solve the master equation for the interaction between a single-mode quantized field and a single mechanical mode of a moving mirror, which is coupled to a zero-temperature reservoir that damps its amplitude. The solution we provide allows for its application in any initial state of the combined system. Furthermore, we obtain solutions to the stationary master equation for an initial number state for the field that is consistent with the result obtained for the average number of phonons. Full article
(This article belongs to the Special Issue 100 Years of Quantum Mechanics)
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22 pages, 351 KiB  
Article
On the Holographic Spectral Effects of Time-Interval Subdivisions
by Sky Nelson-Isaacs
Quantum Rep. 2025, 7(1), 14; https://doi.org/10.3390/quantum7010014 - 19 Mar 2025
Viewed by 365
Abstract
Drawing on formal parallels between scalar diffraction theory and quantum mechanics, it is demonstrated that quantum wavefunction propagation requires a holographic model of time. Measurable time manifests between interactions as a duration which is encoded in the frequency domain. It is thus a [...] Read more.
Drawing on formal parallels between scalar diffraction theory and quantum mechanics, it is demonstrated that quantum wavefunction propagation requires a holographic model of time. Measurable time manifests between interactions as a duration which is encoded in the frequency domain. It is thus a unified entity, and attempts to subdivide these intervals introduce oscillatory artifacts or spectral broadening, altering the system’s physical characteristics. Analogous to spatial holograms, where information is distributed across interference patterns, temporal intervals encode information as a discrete whole. This framework challenges the concept of continuous time evolution, suggesting instead that discrete trajectories define a frequency spectrum which holographically constructs the associated time interval, giving rise to the experimentally observed energy spread of particles in applications such as time-bin entanglement, ultra-fast light pulses, and the temporal double slit. A generalized model of quantum wavefunction propagation based on recursive Fourier transforms is discussed, and novel applications are proposed, including starlight analysis and quantum cryptography. Full article
(This article belongs to the Special Issue 100 Years of Quantum Mechanics)
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21 pages, 295 KiB  
Article
Unveiling the Fifth Dimension: A Novel Approach to Quantum Mechanics
by Frederick George Astbury
Quantum Rep. 2025, 7(1), 8; https://doi.org/10.3390/quantum7010008 - 15 Feb 2025
Viewed by 638
Abstract
Quantum mechanics (QM) has long challenged our understanding of time, space, and reality, with phenomena such as superposition, wave–particle duality, and quantum entanglement defying classical notions of causality and locality. Despite the predictive success of QM, its interpretations—such as the Copenhagen and many-worlds [...] Read more.
Quantum mechanics (QM) has long challenged our understanding of time, space, and reality, with phenomena such as superposition, wave–particle duality, and quantum entanglement defying classical notions of causality and locality. Despite the predictive success of QM, its interpretations—such as the Copenhagen and many-worlds interpretations—remain contentious and incomplete. This paper introduces Strip Theory, a novel framework that reconceptualises time as a two-dimensional manifold comprising foretime, the sequential dimension, and sidetime, an orthogonal possibility dimension representing parallel quantum outcomes. By incorporating sidetime, the theory provides a unified explanation for quantum superposition, coherence, and interference, resolving ambiguities associated with wavefunction collapse. The methods involve extending the mathematical formalism of QM into a five-dimensional framework, where sidetime is explicitly encoded alongside spatial and sequential temporal dimensions. The principal findings demonstrate that this model reproduces all measurable results of QM while addressing foundational issues, offering a clearer and more deterministic interpretation of quantum phenomena. Furthermore, the framework provides insights into quantum coherence, wave–particle duality, and the philosophical implications of free will. These results suggest that Strip Theory can serve as a bridge between interpretations and provide a deeper understanding of time and reality, advancing both theoretical and conceptual horizons. Full article
(This article belongs to the Special Issue 100 Years of Quantum Mechanics)
6 pages, 243 KiB  
Article
Spin Helicity and the Disproof of Bell’s Theorem
by Bryan Sanctuary
Quantum Rep. 2024, 6(3), 436-441; https://doi.org/10.3390/quantum6030028 - 21 Aug 2024
Viewed by 1347
Abstract
Under the quaternion group, Q8, spin helicity emerges as a crucial element of the reality of spin and is complementary to its polarization. We show that the correlation in EPR coincidence experiments is conserved upon separation from a singlet state and [...] Read more.
Under the quaternion group, Q8, spin helicity emerges as a crucial element of the reality of spin and is complementary to its polarization. We show that the correlation in EPR coincidence experiments is conserved upon separation from a singlet state and distributed between its polarization and coherence. Including helicity accounts for the violation of Bell’s Inequalities without non-locality, and disproves Bell’s Theorem by a counterexample. Full article
(This article belongs to the Special Issue 100 Years of Quantum Mechanics)
17 pages, 849 KiB  
Article
EPR Correlations Using Quaternion Spin
by Bryan Sanctuary
Quantum Rep. 2024, 6(3), 409-425; https://doi.org/10.3390/quantum6030026 - 13 Aug 2024
Cited by 1 | Viewed by 2010
Abstract
We present a statistical simulation replicating the correlation observed in EPR coincidence experiments without needing non-local connectivity. We define spin coherence as a spin attribute that complements polarization by being anti-symmetric and generating helicity. Point particle spin becomes structured with two orthogonal magnetic [...] Read more.
We present a statistical simulation replicating the correlation observed in EPR coincidence experiments without needing non-local connectivity. We define spin coherence as a spin attribute that complements polarization by being anti-symmetric and generating helicity. Point particle spin becomes structured with two orthogonal magnetic moments, each with a spin of 12—these moments couple in free flight to create a spin-1 boson. Depending on its orientation in the field, when it encounters a filter, it either decouples into two independent fermion spins of 12, or it remains a boson and precedes without decoupling. The only variable in this study is the angle that orients a spin on the Bloch sphere, first identified in the 1920s. There are no hidden variables. The new features introduced in this work result from changing the spin symmetry from SU(2) to the quaternion group, Q8, which complexifies the Dirac field. The transition from a free-flight boson to a measured fermion causes the observed violation of Bell’s Inequalities and resolves the EPR paradox. Full article
(This article belongs to the Special Issue 100 Years of Quantum Mechanics)
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26 pages, 1741 KiB  
Article
Eliminating the Second-Order Time Dependence from the Time Dependent Schrödinger Equation Using Recursive Fourier Transforms
by Sky Nelson-Isaacs
Quantum Rep. 2024, 6(3), 323-348; https://doi.org/10.3390/quantum6030021 - 25 Jun 2024
Cited by 1 | Viewed by 1657
Abstract
A strategy is developed for writing the time-dependent Schrödinger Equation (TDSE), and more generally the Dyson Series, as a convolution equation using recursive Fourier transforms, thereby decoupling the second-order integral from the first without using the time ordering operator. The energy distribution is [...] Read more.
A strategy is developed for writing the time-dependent Schrödinger Equation (TDSE), and more generally the Dyson Series, as a convolution equation using recursive Fourier transforms, thereby decoupling the second-order integral from the first without using the time ordering operator. The energy distribution is calculated for a number of standard perturbation theory examples at first- and second-order. Possible applications include characterization of photonic spectra for bosonic sampling and four-wave mixing in quantum computation and Bardeen tunneling amplitude in quantum mechanics. Full article
(This article belongs to the Special Issue 100 Years of Quantum Mechanics)
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