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The matrix perturbation method in quantum mechanics

Record Type:	Electronic resources : Monograph/item
Title/Author:	The matrix perturbation method in quantum mechanics/ by Francisco Soto-Eguibar, Braulio Misael Villegas-Martinez, Hector Manuel Moya-Cessa.
Author:	Soto-Eguibar, Francisco.
other author:	Villegas-Martinez, Braulio Misael.
Published:	Cham :Springer International Publishing : : 2023.,
Description:	xv, 190 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	Chapter 1. Standard time-independent perturbation theory -- Chapter 2. Standard time-dependent perturbation theory -- Chapter 3. The matrix perturbation method -- Chapter 4. Examples of the matrix perturbation method -- Chapter 5. Applications of the Matrix Perturbation Method -- Chapter 6. The matrix Perturbation Method for the Lindblad master equation -- Chapter 7. Eliminating the time dependence for a class of time-dependent Hamiltonians.
Contained By:	Springer Nature eBook
Subject:	Perturbation (Quantum dynamics) -
Online resource:	https://doi.org/10.1007/978-3-031-48546-6
ISBN:	9783031485466

The matrix perturbation method in quantum mechanics
Soto-Eguibar, Francisco.

The matrix perturbation method in quantum mechanics[electronic resource] /by Francisco Soto-Eguibar, Braulio Misael Villegas-Martinez, Hector Manuel Moya-Cessa. - Cham :Springer International Publishing :2023. - xv, 190 p. :ill. (some col.), digital ;24 cm.

Chapter 1. Standard time-independent perturbation theory -- Chapter 2. Standard time-dependent perturbation theory -- Chapter 3. The matrix perturbation method -- Chapter 4. Examples of the matrix perturbation method -- Chapter 5. Applications of the Matrix Perturbation Method -- Chapter 6. The matrix Perturbation Method for the Lindblad master equation -- Chapter 7. Eliminating the time dependence for a class of time-dependent Hamiltonians.

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.

ISBN: 9783031485466

Standard No.: 10.1007/978-3-031-48546-6doiSubjects--Topical Terms:

536959
Perturbation (Quantum dynamics)

LC Class. No.: QC174.17.P45

Dewey Class. No.: 530.12

The matrix perturbation method in quantum mechanics
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100 1 $a Soto-Eguibar, Francisco. $3 3672275
245 1 4 $a The matrix perturbation method in quantum mechanics $h [electronic resource] / $c by Francisco Soto-Eguibar, Braulio Misael Villegas-Martinez, Hector Manuel Moya-Cessa.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2023.
300 $a xv, 190 p. : $b ill. (some col.), digital ; $c 24 cm.
505 0 $a Chapter 1. Standard time-independent perturbation theory -- Chapter 2. Standard time-dependent perturbation theory -- Chapter 3. The matrix perturbation method -- Chapter 4. Examples of the matrix perturbation method -- Chapter 5. Applications of the Matrix Perturbation Method -- Chapter 6. The matrix Perturbation Method for the Lindblad master equation -- Chapter 7. Eliminating the time dependence for a class of time-dependent Hamiltonians.
520 $a 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.
650 0 $a Perturbation (Quantum dynamics) $3 536959
650 0 $a Quantum theory. $3 516552
650 1 4 $a Quantum Physics. $3 893952
650 2 4 $a Mathematical Methods in Physics. $3 890898
650 2 4 $a Numerical Analysis. $3 892626
650 2 4 $a Differential Equations. $3 907890
650 2 4 $a Quantum Optics. $3 1066480
700 1 $a Villegas-Martinez, Braulio Misael. $3 3672276
700 1 $a Moya-Cessa, Hector Manuel. $3 3672277
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-3-031-48546-6
950 $a Physics and Astronomy (SpringerNature-11651)