The Matrix Perturbation Method in Quantum Mechanics

Francisco Soto-Eguibar, Braulio Misael Villegas-Martínez, Héctor Manuel Moya-Cessa

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English

Springer International Publishing AG
20 January 2024

Differential calculus & equations; Numerical analysis; Light (optics); Quantum physics (quantum mechanics & quantum field theory); Mathematical physics

This book provides an alternative approach to time-independent perturbation theory in non-relativistic quantum mechanics. It allows easy application to any initial condition because it is based on an approximation to the evolution operator and may also be used on unitary evolution operators for the unperturbed Hamiltonian in the case where the eigenvalues cannot be found. This flexibility sets it apart from conventional perturbation theory. The matrix perturbation method also gives new theoretical insights; for example, it provides corrections to the energy and wave function in one operation. Another notable highlight is the facility to readily derive a general expression for the normalization constant at m-th order, a significant difference between the approach within and those already in the literature. Another unique aspect of the matrix perturbation method is that it can be extended directly to the Lindblad master equation. The first and second-order corrections are obtained for this equation and the method is generalized for higher orders. An alternative form of the Dyson series, in matrix form instead of integral form, is also obtained. Throughout the book, several benchmark examples and practical applications underscore the potential, accuracy and good performance of this novel approach. Moreover, the method's applicability extends to some specific time-dependent Hamiltonians. This book represents a valuable addition to the literature on perturbation theory in quantum mechanics and is accessible to students and researchers alike.

By: Francisco Soto-Eguibar, Braulio Misael Villegas-Martínez, Héctor Manuel Moya-Cessa
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 2023 ed.
Dimensions: Height: 235mm, Width: 155mm,
Weight: 483g
ISBN: 9783031485459
ISBN 10: 3031485459
Pages: 190
Publication Date: 20 January 2024
Audience: College/higher education , Further / Higher Education
Format: Hardback
Publisher's Status: Active

Francisco Soto-Eguibar did his doctoral thesis on the foundations of quantum mechanics. He is currently a researcher in the quantum optics group of the National Institute of Astrophysics, Optics and Electronics (INAOE). He has published around 80 articles in international peer reviewed journals and 3 books. He teaches courses on quantum mechanics and electromagnetic theory. Hector M. Moya-Cessa obtained his PhD at Imperial College in 1993 and since then he is a researcher/lecturer at Instituto Nacional de Astrofísica, Óptica y Electrónica in Puebla, Mexico where he works on Quantum Optics. He has published over 200 articles in international peer reviewed journals. He is a fellow of the Alexander von Humboldt Foundation. Braulio Misael Villegas-Martínez is a researcher at the Center for Research in Engineering and Applied Science (CIICAp-UAEM), in Cuernavaca, Mexico. His research interests include quantum optics, PT symmetry, and waveguides. Villegas-Martinez received his PhD in Optical Sciences from the National Institute of Astrophysics, Optics, and Electrónics (INAOE).

Reviews for The Matrix Perturbation Method in Quantum Mechanics

“Throughout the book, the validity of the perturbative results are assessed by comparison with either exact (if available) or numerically computed solutions for the respective systems. ... readers who prefer to see all details of a calculation and explicit formulas probably will like this book.” (H. Hogreve, Mathematical Reviews, June, 2025)