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Lecture 5: perturbation methods

Lecture 5: perturbation methods
Lecture 5: perturbation methods
In this lecture, I give a short and essential overview of some important approximation theories and mathematical tricks used in spin dynamics to cope with otherwise intractable problems. I discuss perturbation theory, average Hamiltonian theory and interaction frame transformations. Perturbation theory is used to find approximate solutions to complex or insoluble eigenvalue problems when the Hamiltonian can be divided into a large, unperturbed, and a small, perturbation, term. Average Hamiltonian theory provides an approximate solution to the Liouville–von Neumann equation when the Hamiltonian is time-dependent. An interaction frame transformation is a recipe for deriving the form that Hamiltonians assume when the reference frame is transformed by rotations.
59-69
Royal Society of Chemistry
Pileio, Giuseppe
13f78e66-0707-4438-b9c9-6dbd3eb7d4e8
Pileio, Giuseppe
Pileio, Giuseppe
13f78e66-0707-4438-b9c9-6dbd3eb7d4e8
Pileio, Giuseppe

Pileio, Giuseppe (2022) Lecture 5: perturbation methods. In, Pileio, Giuseppe (ed.) Lectures On Spin Dynamics: The Theoretical Minimum. (RSC eTextbook Collection) Royal Society of Chemistry, pp. 59-69. (doi:10.1039/9781837670871-00059).

Record type: Book Section

Abstract

In this lecture, I give a short and essential overview of some important approximation theories and mathematical tricks used in spin dynamics to cope with otherwise intractable problems. I discuss perturbation theory, average Hamiltonian theory and interaction frame transformations. Perturbation theory is used to find approximate solutions to complex or insoluble eigenvalue problems when the Hamiltonian can be divided into a large, unperturbed, and a small, perturbation, term. Average Hamiltonian theory provides an approximate solution to the Liouville–von Neumann equation when the Hamiltonian is time-dependent. An interaction frame transformation is a recipe for deriving the form that Hamiltonians assume when the reference frame is transformed by rotations.

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Published date: 13 June 2022

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Local EPrints ID: 478708
URI: http://eprints.soton.ac.uk/id/eprint/478708
PURE UUID: 942b8a99-135b-477f-a60b-ca71b2674288
ORCID for Giuseppe Pileio: ORCID iD orcid.org/0000-0001-9223-3896

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Date deposited: 07 Jul 2023 16:41
Last modified: 18 Mar 2024 03:02

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Author: Giuseppe Pileio ORCID iD
Editor: Giuseppe Pileio

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