Open AccessTowards time-dependent wave packet tunnelling via complex Riccati equations
Author(s) -
M Bonilla-Licea,
Dieter Schuch
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1612/1/012005
Subject(s) - quantum tunnelling , wave packet , superposition principle , gaussian , transmission (telecommunications) , riccati equation , network packet , matrix (chemical analysis) , statistical physics , quantum , quantum mechanics , physics , mathematics , computer science , differential equation , telecommunications , computer network , materials science , composite material
Since the discovery of tunnelling in the early days of quantum mechanics, there has been considerable interest in finding an effective method to determine the transmission of wave packets through a potential barrier. In this work, we combine the transfer matrix method, known from stationary tunnelling problems, with the construction of Gaussian wave packets via superposition of stationary states with the knowledge about the dynamics of generalized Gaussian-shaped coherent states in terms of complex Riccati equations. In the low-energy regime, this leads to an approximate analytical expression for the transmission probability and its dynamics. Extension to more general potential shapes appears straightforward.