Solving the von Neumann equation with time-dependent Hamiltonian. Part I: Method
Mathematical Physics
2008-05-30 v1 math.MP
Abstract
The unitary operators U(t), describing the quantum time evolution of systems with a time-dependent Hamiltonian, can be constructed in an explicit manner using the method of time-dependent invariants. We clarify the role of Lie-algebraic techniques in this context and elaborate the theory for SU(2) and SU(1,1). We show that the constructions known as Magnus expansion and Wei-Norman expansion correspond with different representations of the rotation group. A simpler construction is obtained when representing rotations in terms of Euler angles. The many applications are postponed to Part II of the paper.
Keywords
Cite
@article{arxiv.0805.4487,
title = {Solving the von Neumann equation with time-dependent Hamiltonian. Part I: Method},
author = {Maciej Kuna and Jan Naudts},
journal= {arXiv preprint arXiv:0805.4487},
year = {2008}
}
Comments
14 pages