Posting Number S06676P
Position Title Postdoctoral Research Associate
Functional Title Postdoctoral Research Associate
Department Materials Science and Engineering
Salary Range $45,000 DOQ
Pay Basis Monthly
Position Status Regular full-time
Location Richardson
Position End Date (if temporary)
Posting Open Date 10/16/2025
Posting Close Date
Open Until Filled Yes
Desired Start Date 11/10/2025
Job Summary
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:
Minimum Education and Experience
Ph.D in a related field.
Preferred Education and Experience
Ph.D. in Mathematics
Other Qualifications
To the extent this position requires the holder to research, work on, or have access to critical infrastructure as defined in Section 117.001(2) of the Texas Business and Commerce Code, the ability to maintain the security or integrity of the critical infrastructure is a minimum qualification to be hired and to continue to be employed in the position.
Essential Duties and Responsibilities
Physical Demands and Working Conditions
Physical Activities
Working Conditions
Additional Information
A remote work schedule is not available for this position.
What We Can Offer
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Visit https://hr.utdallas.edu/employees/benefits/ for more information.
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Special Instructions Summary
Important Message
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