**5. Conclusion**

We performed the calculations of the electronic structure for the graphitic nanocone and the graphene wormhole. In the first case, our aim was to find the quadratically integrable solution that includes the boundary effects and considers the real geometry. This goal was partially achieved, but we need to verify the properties of the found solution close to the tip. The precision of the calculations could be improved by the better choice of the corresponding geometry, by the consideration of the discretion of the energetic spectrum coming from the finite size of the nanostructure, and by the inclusion of next effects coming from the overlap of the neighboring atomic orbitals close to the tip [2]. The localization of the electrons shown in **Figures 11** and **12**, especially in the case of three defects, makes the graphitic nanocone a possible candidate for the construction of the scanning probe in atomic force microscopy.

In the second case of the graphene wormhole, we presented the mathematical motivation for our prediction of the effects that should appear close to the wormhole bridge. Our predic‐ tions will be verified with the help of the geometric optimizations and ab initio calculations. On this base, the most suitable candidates for the experiments will be chosen.
