Among these four fields the most important contribution was made into the
theory of resonances.
We derived new equations which are equivalent to the Schrödinger equation, but are more convenient for practical computations. They are linear first order differential equations with simple boundary conditions. Solving them one obtains the wave function and the Jost function at the same time, for any given values of complex momentum and angular momentum. Therefore bound and resonant states can be located in a unified way, simply as zeros of the Jost function. In deriving these equations the asymptotic exponential behaviour of the wave function is analytically factorized, which makes the equations more stable and therefore significantly improves the accuracy in numerical calculations. Moreover, it guarantees correct behaviour of the solution at large distances with any complex momentum.
We have developed this method into a full theory with all necessary proofs and generalized it to treat all complications arising with multichannel, Coulomb, and singular potentials.
When applied to semiconductor nanostructures, in contrast to the existing methods for locating resonances, the Jost function approach is exact (within the envelope-function approximation, of course) and treats the bound and all types of resonant states in a uniform way as the S-matrix poles in the complex energy plane. The effect of the external electric field can also be included in an exact way.

I am sure that in the future our equations will be included in all new textbooks on quantum mechanics and scattering theory.

In the -meson physics
we were the first who did a rigorous analysis of the -nucleus dynamics. In our publications we dismissed the constraint for a quasi-bound state formation. This stimulated experimental as well as theoretical investigations of the -meson interaction with light nuclei. We located the -matrix poles, and predicted the near-threshold eta-deuteron resonance. There are many experimental evidences supporting the existence of such resonance, and our calculations were met with much interest by the experimental groups working in this field.
Thus, our contribution to -nucleus physics is clear and noteworthy. It definitely extended the knowledge in this field and indicated the directions for further investigations.

In nuclear astrophysics
we came with a new idea of extending the standard model of the nucleosynthesis in stellar plasma. This especially concerns the Big Bang theory where the conditions (temperature and density) are favourable for the three-body reactions to occur. Our calculations show that this very important theory of the creation of universe needs to be revised.
Thus, we indicated a new direction for further investigations in this field.

Investigating nuclear fusion in molecules,
we found that under certain conditions the nuclei constituting the molecule can fuse at a very high rate. This happens if the resulting compound nucleus has an excited state near the threshold energy for the inverse process. As an example of such molecule, we indicated a (very surprising) possibility of water burning. In general, our finding indicates a new possibility of making a cold fusion and, therefore, a new direction for further investigations in this field.