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The European Physical Journal A

Phase factors in bases for solutions of time-dependent schr�dinger equations

Hans–Christian Pauli, L. Wilets

Published Mar 1, 1976• 15 citations
Publisher
DOI
10.1007/bf01547506

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The perturbative evaluation of the time-dependent quantum transport is investigated by making use of the Lewis-Riesenfeld invariant theory and the invariant-related unitary transformation formulation in this paper.We obtain the complete set of solutions of the time-dependent Schrdinger equation governing the behaviour of electrons in a double-well structure. Based on these exact solutions,we obtain the first-order quantum rate equation by regarding the interaction Hamiltonian between the double-well structures and the heat reservoirs as the perturbative Hamiltonian.An approach to the geometric phase factor (Berry's phase factor) in the adiabatic quantum transport process is briefly discussed in this paper.We hold that the formulation presented here has advantages in dealing with transport problem over the method proposed by Gurvitz et al.
Web-Schr{ö}dinger is an interactive client-server software for the solution of the time-dependent and time-independent (stationary) Schr{ö}dinger equation. The program itself runs on a server computer and can be used through the Internet with a simple Web browser. Nothing is installed on the user's computer. The user can load, run, and modify ready-made example files, or prepare her/his own configuration(s), which can be saved on her/his own computer for later use. Several users can access the program parallelly and each can have independent sessions. Typical run times are in the second, or minute range.