Canonical form of the Evolution Operator of a Time-Dependent Hamiltonian in the Three Level System

Kazuyuki Fujii

Canonical form of the Evolution Operator of a Time-Dependent Hamiltonian in the Three Level System

Mathematical Physics 2011-06-21 v1 math.MP Quantum Physics

Authors: Kazuyuki Fujii

Abstract

In this paper we study the evolution operator of a time-dependent Hamiltonian in the three level system. The evolution operator is based on $SU(3)$ and its dimension is $8$ , so we obtain three complex Riccati differential equations interacting with one another (which have been obtained by Fujii and Oike) and two real phase equations. This is a canonical form of the evolution operator.

Keywords

evolution operator time-dependent hamiltonian three level system su(3) riccati differential equations canonical form

Cite

@article{arxiv.1008.4624,
  title  = {Canonical form of the Evolution Operator of a Time-Dependent Hamiltonian in the Three Level System},
  author = {Kazuyuki Fujii},
  journal= {arXiv preprint arXiv:1008.4624},
  year   = {2011}
}

Comments

Latex 10 pages; no figure

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