Real time quantum tunneling through a double square barier

• Autorzy: Papadopoulos George J.

Identyfikatory

DOI

10.34808/19qb-zg64

• Języki publikacji: EN

Abstrakty

EN

The propagator of a one-dimensional double square barrier is obtained analytically in terms of the relevant eigenfunctions. With the aid of the propagator the wavefunction evolution for a particle, initially in a state of wave packet, located on the left-hand side of the barrier, with ignorable overlap with the barrier, is obtained. There follows study of the probability and current densities stemming from the particle initial state. In particular, the space distribution sat given times of the above densities are given. Furthermore, their evolution in time at the entrance and exit of the barrier is obtained. The numerical results show repeated reversal in the current density at the barrier entrance, while being unidirectional at the exit. However, the probability of entering the barrier over an extremely long time tends to equal the corresponding probability of exiting the barrier. Owing to the fact that the wave packet expands on both of its sides, as time goes by, it is possible to have transmission even if the particle’s initial momentum points away from the barrier. The effect, in question, becomes evident in diagrams for the transmitted probability beyond the barrier exit in terms of the particle initial momentum, over a region.

Słowa kluczowe

EN

double square barrier propagator; probability density; current density; wave packet; probability

PL

gęstość prawdopodobieństwa; gęstość prądu; pakiet falowy; prawdopodobieństwo

• Wydawca: Politechnika Gdańska
• Czasopismo: TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
• Rocznik: 2023
• Tom: Vol. 27, No 3
• Strony: 1--8
• Opis fizyczny: Bibliogr. 4 poz., wykr.

Twórcy

autor

Papadopoulos George J.

• Department of Physics, Solid State Physics Section, National and Kapodistrian University of Athens, Panepistimiopolis, Athens157 84 Zografos, Athens, Greece

• https://orcid.org/0000-0001-9250-4916

Bibliografia

• [1] G. J. Papadopoulos, “Real time quantum tunneling,” TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk, vol. 19, no. 1, pp. 65–74, 2015.
• [2] V. Petrillo and V. Olkhovsky, “Tunnelling time of a gaussian wave packet through two potential barriers,” Central European Journal of Physics, vol. 3, no. 3, pp. 339–350, 2005.
• [3] H. Guo, K. Diff, G. Neofotistos, and J. Gunton, “Time-dependent investigation of the resonant tunneling in a double-barrier quantum well,” Applied physics letters, vol. 53, no. 2, pp. 131–133, 1988.
• [4] S. Cordero and G. Garcia-Calderon, “Transient effects and reconstruction of the energy spectra in the time evolution of transmitted gaussian wave packets,” Journal of Physics A: Mathematical and Theoretical, vol. 43, no. 18, p. 185301, 2010.