Mathematical description of quantum mechanics

kvantove grafyThe accurate prediction of many physical phenomena depends on the mathematical accuracy of quantum mechanical  formulation. We develop mathematical theory for such a description (e.g., the theory of  non-group operators), and its application to various systems, such as quantum graphs and quantum wave channels.

Quantum mechanical systems are often described by Hamiltonians  which give reasonable predictions thanks to physical symmetries rather than mathematical  postulates of isogroups. A number of methods  of  non-group  operator analysis fails, therefore we look for new techniques and generalise the classical ones.

The theoretical description of many real world situations is so complex that there is a need for simplification and theoretical models. Such models include quantum graphs and singular interactions.  With them, we can describe, for instance, short-range nuclear interactions or the movement of an electron in an organic substance.

The simplest case of quantum graphs is the quantum wave channel., i.e., a tube. We study  how the wave channel  geometry (reflected, curved) influences  the  energy spectrum of particles moving inside the wave channel.

Group Members

Faculty

prof. RNDr. Pavel Exner, DrSc.
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prof. Ing. Jiří Tolar, DrSc.
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RNDr. Ing. Michal Jex, Ph.D.
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External co-workers

Mgr. David Krejčiřík, DSc.
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prom. fyz. Miroslav Znojil, DrSc.
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Students

Ing. Radek Novák
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Supervisor: Mgr. David Krejčiřík, Ph.D., DSc.
Topic: Nehermitovské operátory v kvantové mechanice