Computational method for the long time propagation of quantum channeled particles in crystals and carbon nanotubes

This work reports on the computational method for the long time propagation of the quantum channeled particles in infinite and finite harmonic interaction wells and in a realistic carbon nanotube interaction potential well. This method is based on the Chebyshev global propagation method for solving of the corresponding time dependent Schrödinger equation. For comparison, the computational method based on the Crank-Nicolson propagation method is also presented. In the case of quantum particle motion in infinite harmonic potential well, when the analytical solution of the corresponding time-dependent Schrödinger equation exists, we show that the obtained propagation method is efficient, very accurate and numerically stable. It is superior with respect to the method based on the Crank-Nicolson propagation method. A detailed study of the long time quantum particle motion in the finite harmonic interaction potential well shows that the obtained computational method based on the Chebyshev global propagation method can be successfully applied for following of the channeled quantum particle in crystals and carbon nanotubes. This is demonstrated in the case of quantum particle motion in a realistic carbon nanotube interaction potential well.