The propagation of wave packets of quantum particles through porous structures in thin semi-transparent films is studied. Numerical solution of the nonstationary Schrödinger equation is used in two-dimensional (for slits) and three-dimensional (round holes) cases. The transmission coefficient of quantum particles is compared with that of classical particles with the same density distribution. The vortex motion of the flux density having a hydrodynamic analog is studied. A variant of the “quantum caustic” is considered upon scattering of the particle wave packet at an obstacle.

The processes of the propagation of quantum and classical charged particles through porous films are studied. The propagation of quantum particles is analyzed by numerically calculating the Schrödinger equation. The polarization force acting on the charge is calculated within the framework of classical electrodynamics. The possibility of pore formation in the films is analyzed in the problem of the propagation of ions with large charges through ultrathin carbon films. Mathematical modeling of the film accompanied by elucidation of the most important polarization properties is carried out to understand the process more clearly. The calculations show the possibility of film perforation because of the action of ponderomotive forces generated by the strong polarization field of the wave packet of the passing ion.

The exact potentials of the interaction of channeled hydrogen atoms with non-chiral carbon nanotubes of $$\left( {n,0} \right)$$ and $$\left( {n,n} \right)$$ types are calculated using the Lennard-Jones potential. After expansion in a two-dimensional Fourier series of one-dimensional reciprocal lattice vectors and azimuthal harmonics, these potentials are used to analyze the motion of atoms in the channel. Numerical solution of the Schrödinger equation with the averaged electrostatic interaction potential for a $$\left( {10,10} \right)$$ nanotube ensures discrete transverse energy levels and corresponding wave functions. The evolution of the spatial distribution of channeled hydrogen atoms moving in the longitudinal direction under the influence of the periodic perturbing interaction potential as a function of the longitudinal velocity is studied by means of fundamental solution of the kinetic equation. The ability to induce the focusing effect at the center of a nanotube for moving hydrogen atoms is shown as well.

The process of the perforation of a nanometer-thick film during passage of the wave packet of a multicharged ion is studied. It is shown that the resonant behavior of vibrations of the disk released from the film has a significant effect on the perforation process. The resonance mechanism is based on the “push-pull” process. A model of the strength of the polarization interaction between the film and the wave packet of the particle is proposed. The model makes it possible to estimate the threshold value of the force required to form a pore during the passage of a multicharged ion through the film.

Fields of polarization that appear during the penetration of multiply charged ions through ultrathin nanomembranes are calculated by means of classical electrodynamics. The ponderomotive forces generated by these fields are able to press pores out of membranes. The dimensions of the penetrating ions’ wave packets determine the sizes of these pores. Calculations describe the experimental data on penetration through one film and through a system of four parallel films.

The interaction between an atom located inside a crystal structure and a moving external particle is accompanied by changes in its environment, and as a consequence, the atom is additionally affected by it. The force impact of the image of a moving multiply charged ion on the state of an ultrathin carbon film is calculated. The p possibility of forming a pore in the film as a result of ion propagation through the film is shown. The size of the pore turns out to be strictly correlated with that of the ion wave packet incident from free space on the thin-film carbon crystal structure. It is possible to trace the formation of the boundary with a classically inaccessible region called the caustic surface by numerically solving the three-dimensional nonstationary Schrödinger equation in the problem of the collision between a moving multiply charged ion and a carbon atom. On the whole, the performed calculation confirms the previously obtained results.

Low energy particle channeling through single-wall carbon nanotubes 245nm long with (20,0)/(10,10) heterojunction has been studied. As demonstrated the ion beam cross-section becomes half the area after beam passage through the heterojunction.

Peculiarities of the tunneling conduction of electrons in systems of quantum wells and barriers are studied numerically on the basis of the laws of quantum mechanics

Phenomena arising during the passage of a particle through a cylindrical structure are considered. The pore formation in a very thin film by the moving of highly charged ions, as well as the enhanced probability of the particle passage through a porous structure, is discussed.

The problem of pore formation during the propagation of Xe+q ions with energies of around 50 keV and charges q = 20–54 through an ultrathin carbon film is discussed. The results from calculations suggest that pore formation can be attributed to the perforation of part of a bombarded film by the moving wave packet of a xenon ion with a sufficiently high charge.

The inelastic collisions effect on the interaction of the projectile with a super thin solid film is considered. The wave nature of the particle and its transitions from delocalized to the strongly localized state defined many important properties of the interaction. As examples the effect of perforation the 1nm carbon foil as well as the overwhelming passage through a thick porous layer are considered.