Academic Research

One of the most fundamental principles of quantum mechanics seems to be that all operators that are associated with an observable must be Hermitian. The simple motivation appears to be the fact that physical observables should be real numbers. However, as appealing this argument seems to be on the first glance, it is not necessary true. In fact, already almost 50 years ago it was shown that the known Hamiltonians describing, e.g., atoms, molecules, solids, etc. can in a mathematically strict way be continued into the complex plane. Surprisingly, this leads to a consistent description of bound and unbound (continuum) states and thus there is no need for introducing by hand some trick to handle the non-square-integrable continuum states as is needed in standard scattering theory. The price to pay for the consistent description is the loss of hermiticity. On the other hand, besides provision of the advantage of a consistent description, this alternative formulation also allows for the efficient solution of a number of scattering problems. In this project, this efficiency gain should be investigated in a systematic fashion for a specific problem.

The student will be introduced into the underlying physics and the use of computer codes developed in our research group that she/he will learn to apply them within an on-going research project. Depending on qualification and interest, the student may also write a small new code or extend an existing code.

Advanced undergraduate students (at least 2nd year)
Graduate students
PhD students

The student should 

Some previous experience in computer coding is helpful, but not required.