William Vandenberghe
1 year ago
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Mathematics, Quantum Mechanics University of Texas at Dallas in United States
Degree Level
Postdoc
Field of study
Mathematics
Funding
not provided
Deadline
Oct 18, 2026
Country
United States
University
University of Texas at Dallas
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About this position
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Summary:
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Details
Posted: 18-Oct-25
Location: Richardson, Texas
Categories:
Research - Laboratory/Non-Laboratory
Staff/Administrative
Internal Number: 30540
Posting Number: S06676P
Job Description:
Looking for a post-doctoral Research Associate to perform full-time mathematical research with the goal of developing a practical yet rigorous mathematical framework for quantum mechanics. The researcher is expected to make contributions in the fields of functional analysis, complex analysis, spectral theory, and partial-differential equations, but also applications in number theory are of interest.
Typically, the theory of quantum mechanics relies on the Hilbert space of square-integrable functions (L2) but when the domain space is not compact (e.g. L2 ), or the potential is singular, the eigenfunctions are not contained in the Hilbert space (e.g. e^(ikx)). In spectral theory, the absence of eigenvectors in the Hilbert space is typically circumvented by using a projection-valued measure. In the field of topological vector spaces, the problem is addressed using the nuclear spectral theorem which is set in the rigged Hilbert space (Gelfand's triple) but the requirements imposed on the Schrodinger operator are non-trivial. Finally, the theory of non self-adjoint operators is very poorly developed. Current practice in physics is typically to ignore mathematical rigor because an easily accessible mathematical theory is lacking.
Our goal is to develop a mathematically rigorous framework applicable to the Schrodinger equation where eigenvectors are tempered distributions (topological dual of the Schwartz space). The developed framework should be mathematically rigorous yet accessible to the physics community and applicable to existing problems in physics. As applications, open problems in the field of number theory, such as the Dirichlet divisor problem, the Riemann hypothesis (e.g., through the Hilbert-Polya conjecture) are also of interest.
The position would have weekly meetings with prof. William Vandenberghe to discuss research progress and novel research directions.
If interested, the research associate can also:
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About The University of Texas at Dallas
The University of Texas at Dallas is an innovative institution in the heart of North Texas on the path to achieving Tier One national research university status.UT Dallas has grown since its founding in 1969 to include 132 degree programs, with cutting-edge curricula serving a variety of undergraduate and graduate student interests.The University continues its original commitment to providing some of the state's most-lauded science and engineering programs and has also gained prominence for a breadth of educational paths, from criminology to biomedical engineering to arts and technology.The wealth of learning resources available to UT Dallas students is the result of a concentrated effort to attract the top minds on both ends of the classroom relationship. Joining the faculty's Nobel laureate and four National Academies members since 2005 are more than 200 tenure and tenure-track professors hailing from the world's best colleges, including Harvard, MIT, Cambridge and Columbia University. In addition, UT Dallas is home to more than 50 centers, labs and institutes that facilitate research and opportunities for hands-on learning. Students, meanwhile, arrive at UT Dallas well-prepared
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to succeed in higher education: In 2011, nearly 39 percent of freshmen ranked in the top 10 percent of their high school class, and 75 percent ranked in the top 25 percent.With an eye on building a future as bright as its beginnings, UT Dallas will continue its push to attain Tier One research university status and produce graduates who are well-equipped to succeed professionally.
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What's required
Applicants should hold a Ph.D. in mathematics, physics, or a closely related field. Experience in functional analysis, complex analysis, spectral theory, and partial differential equations is expected. Interest or background in number theory is desirable. The ability to conduct independent research and collaborate in weekly meetings is required. No specific language or GPA requirements are mentioned.
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Professors
Professor at University of Texas at Dallas
University of Texas at Dallas
Research Interests
Number Theory
Quantum Mechanics
Electron Transport
Spectral Analysis
Functional Analysis
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Prepare your application
Review drafts and confirm requirements with the university.