Unitary transformations depending on a small parameter-Reference-Cited by-同舟云学术

Unitary transformations depending on a small parameter

Published:2011-11-02 Issue:2139 Volume:468 Page:685-700
ISSN:1364-5021
Container-title:Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Proc. R. Soc. A.

Author:

Casas F.¹,Oteo J. A.²,Ros J.²³

Affiliation:

1. Departament de Matemàtiques and IMAC, Universitat Jaume I, E-12071 Castellón, Spain

2. Departament de Física Teòrica, Universitat de València, 46100-Burjassot, València, Spain

3. Instituto de Física Corpuscular (IFIC), Universitat de València-CSIC, Apartado 22085, 46071-Paterna, València, Spain

Abstract

We formulate a unitary perturbation theory for quantum mechanics inspired by the Lie-Deprit formulation of canonical transformations. The original Hamiltonian is converted into a solvable one by a transformation obtained through a Magnus expansion. This ensures unitarity at every order in a small parameter. A comparison with the standard perturbation theory is provided. We work out the scheme up to order ten with some simple examples.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2011.0388

Reference21 articles.

1. The quantum normal form and its equivalents

2. Mathematical Aspects of Classical and Celestial Mechanics

3. Histories of adiabatic quantum transitions

4. Quantum phase corrections from adiabatic iteration

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