Quantum mechanics is arguably the most successful physical theory, leading to a profound understanding of the microscopic world, with implications for almost every field of physics as well as other disciplines. It has also led to an astounding technological advance in our society, a fact highlighted by the United Nations declaration of 2025 as the International Year of Quantum Science and Technology.

Still, despite being a centenary theory, quantum mechanics continues to pose numerous theoretical and mathematical challenges – perhaps even more so with the advent of the so-called "second quantum revolution" (after the corroboration of Bell's theorem) that brought to the fore both new and foundational issues with the structure of the theory. Even though much progress has been made in the last few decades, often through the use of sophisticated and rigorous mathematical methods, much still remains to be understood.

Therefore, the goal of this Research Topic is twofold: to stimulate the investigation of open mathematical and theoretical problems in quantum mechanics; and to encourage the exchange of ideas between different areas of theoretical and mathematical physics, which nonetheless share similar tools, as applied to quantum mechanics. Consequently, we invite contributions from a wide range of topics, such as

• Contact interactions in quantum mechanics, and its applications.
• ⁠Exactly solvable quantum models
• Spectral theory
• Generalized uncertainty principle
• ⁠Pseudo-differential operators in quantum mechanics
• Non-linear Schrödinger equation
• Supersymmetric quantum mechanics
• Theoretical quantum optics

We emphasize that the list of topics above is not exhaustive, and it is meant only as a general guide. In addition, we note that while the focus of the Research Topic is on original contributions, reviews summarizing the state of the art of a given field are also welcome.

Are you interested in contributing a manuscript to this Research Topic?

Recent Mathematical and Theoretical Progress in Quantum Mechanics