Development of Methods in the Theory of Self-adjoint Extensions

• Applicants: Dr. Johannes Friedemann Brasche (†); Dr. Hagen Neidhardt (†)
• Subject Area: Mathematics
• Term: from 2016 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 298815297

Point interactions or zero range potentials in quantum physics are usually described by self-adjoint extensions of a given densely defined closed symmetric operator. An appropriate tool to handle extensions is the boundary triplet approach developed in the last 3 decades. It turns out that this approach gives good results for point interactions. The goal of the proposed project is to apply the boundary triplet approach to point interactions for composite quantum systems. Since Hamiltonians of those systems have a tensor product structure the mathematical problem is to adapt the boundary triplet approach to symmetric operators having a tensor product structure. Finally, we want to demonstrate the strength of the approach by application to several physical problems from quantum mechanics and other areas.

• DFG Programme: Research Grants
• International Connection: Russia
• Cooperation Partner: Professor Dr. Igor Y. Popov