Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
4.6
2.2
Journals
Mathematics
Special Issues
Advances in Mathematics for Quantum Mechanics
share announcement

Advances in Mathematics for Quantum Mechanics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E4: Mathematical Physics".

Deadline for manuscript submissions: 31 May 2026 | Viewed by 2504

Special Issue Editor

Dr. L.S.F. Olavo

E-Mail Website
Guest Editor
UnB/International Centre of Physics, Universidade de Brasília, Brasilia, Brazil
Interests: foundations of quantum mechanics; history of quantum mechanics; philosophy of quantum mechanics

Special Issue Information

Dear Colleagues,

The current year, 2025, has been recognized as the international year for the establishment of quantum mechanics as a systematic and well-developed physical theory. The theory has undergone many technological advances and applications in the last 100 years. However, it still lacks a unified interpretation (if such a thing is possible), and new formal and theoretical developments are proposed regularly.

Thus, we invite you to contribute to this Special Issue titled “Advances in Mathematics for Quantum Mechanics”. We desire original research focused on theoretical and/or mathematical contributions that advance our understanding of quantum mechanics, its interpretation, formalism, and status as a formally based branch of epistemology.

Dr. L.S.F. Olavo
Guest Editor

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 250 words) can be sent to the Editorial Office for assessment.

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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • mathematical foundations of quantum information and computation
  • operator algebras and spectral theory in quantum systems
  • stochastic methods and open quantum systems
  • foundations of quantum mechanics
  • new advances in quantum mechanics
  • formal developments in quantum mechanics
  • philosophical developments in quantum mechanics

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

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

Published Papers (2 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

41 pages, 3112 KB  
Article
A Bird’s-Eye View on a New Stochastic Interpretation of Quantum Mechanics
by Olavo L. Silva Filho and Marcello Ferreira
Mathematics 2025, 13(21), 3571; https://doi.org/10.3390/math13213571 - 6 Nov 2025
Cited by 3 | Viewed by 1108
Abstract
Since the early twentieth century, quantum mechanics has sought an interpretation that offers a consistent worldview. In the course of that, many proposals were advanced, but all of them introduce, at some point, interpretation elements (semantics) that find no correlate in the formalism [...] Read more.
Since the early twentieth century, quantum mechanics has sought an interpretation that offers a consistent worldview. In the course of that, many proposals were advanced, but all of them introduce, at some point, interpretation elements (semantics) that find no correlate in the formalism (syntactics). This distance from semantics and syntactics is one of the major reasons for finding so abstruse and diverse interpretations of the formalism. To overcome this issue, we propose an alternative stochastic interpretation, based exclusively on the formal structure of the Schrödinger equation, without resorting to external assumptions such as the collapse of the wave function or the role of the observer. We present four (mathematically equivalent) mathematical derivations of the Schrödinger equation based on four constructs: characteristic function, Boltzmann entropy, Central Limit Theorem (CLT), and Langevin equation. All of them resort to axioms already interpreted and offer complementary perspectives to the quantum formalism. The results show the possibility of deriving the Schrödinger equation from well-defined probabilistic principles and that the wave function represents a probability amplitude in the configuration space, with dispersions linked to the CLT. It is concluded that quantum mechanics has a stochastic support, originating from the separation between particle and field subsystems, allowing an objective description of quantum behavior as a mean-field theory, analogous, but not equal, to Brownian motion, without the need for arbitrary ontological entities. Full article
(This article belongs to the Special Issue Advances in Mathematics for Quantum Mechanics)
►▼ Show Figures

Figure 1

14 pages, 449 KB  
Article
Local Quantum Uncertainty and Entanglement in the Hyperfine Structure of the Hydrogen Atom: A Lindblad Approach
by Kamal Berrada and Smail Bougouffa
Mathematics 2025, 13(20), 3340; https://doi.org/10.3390/math13203340 - 20 Oct 2025
Cited by 1 | Viewed by 802
Abstract
In this work, we investigate quantum correlations, including entanglement and quantum discord, within the hyperfine structure of the hydrogen atom using the Lindblad master equation to model its dynamics as an open quantum system interacting with an environment. By incorporating realistic environmental influences, [...] Read more.
In this work, we investigate quantum correlations, including entanglement and quantum discord, within the hyperfine structure of the hydrogen atom using the Lindblad master equation to model its dynamics as an open quantum system interacting with an environment. By incorporating realistic environmental influences, we examine the time evolution of two key measures of quantum correlations: concurrence, which quantifies entanglement, and local quantum uncertainty (LQU), a broader indicator of quantumness. Our analysis spans various initial states, including coherent superpositions of hyperfine states, to capture a wide range of possible configurations and demonstrate how these measures capture distinct aspects of quantum behavior. The results reveal the robustness of LQU in regimes where entanglement may vanish. This resilience of LQU underscores its utility as a robust measure of quantum correlations beyond entanglement alone in the hydrogen atom. By elucidating the dynamics of quantum correlations in the hydrogen atom under realistic conditions, this work not only deepens our fundamental understanding of atomic systems but also highlights their potential relevance to quantum information science and the development of quantum technologies. Full article
(This article belongs to the Special Issue Advances in Mathematics for Quantum Mechanics)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-2
Back to TopTop