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Exact Treatment of Finite-Dimensional and Infinite-Dimensional Quantum Systems


Živković, Tomislav P.
Exact Treatment of Finite-Dimensional and Infinite-Dimensional Quantum Systems, Hauppauge: Nova Science Publishers, 2010 (monografija)


Naslov
Exact Treatment of Finite-Dimensional and Infinite-Dimensional Quantum Systems

Autori
Živković, Tomislav P.

Vrsta, podvrsta i kategorija knjige
Autorske knjige, monografija, znanstvena

Izdavač
Nova Science Publishers

Grad
Hauppauge

Godina
2010

Stranica
230

ISBN
978-1-61668-597-3

Ključne riječi
local rank perturbation ; exact treatment ; quantum systems

Sažetak
This book introduces a new method that produces exact solutions of finite- and infinite-dimensional modified systems. In this method, named Low Rank Modification (LRM), eigenvalues and eigenstates of a modified system are expressed in terms of the known eigenvalues and eigenstates of the original system. In this respect LRM is similar to the perturbation approach. However, there are profound differences. Perturbation theory relies on power series expansion, in most cases it produces only an approximate result, and it breaks down if the perturbation is too strong. Advantage of the LRM is that it is exact, regardless of how strong is the perturbation of the original system. Numerical efficiency of LRM depends essentially on the rank of the operators that represent modification of this system, and not on the strength of this modification. LRM applies to almost arbitrary eigenvalue problems. It applies to standard as well to generalized eigenvalue equations. As long as modification of the parent system is represented by finite rank operators, it applies also to infinite-dimensional systems. In addition, it applies to time-independent as well as to time-dependent systems. LRM is particularly suitable for the treatment of those problems where modification of the original system is too large to be treated efficiently within a standard perturbation expansion approach. The method is illustrated with several examples involving finite-dimensional as well as infinite-dimensional systems. As a particular example, vibrational isotope effect in the harmonic approximation is treated within this formalism. Low Rank Modification should offer graduate students as well as research workers a new tool for the treatment of many presently intractable eigenvalue problems as well as a new insight into those eigenvalue problems which can be efficiently solved by some other methods. // Table of Contents: // Preface // Acknowledgments // Chapter 1. Introduction, pp. 3-11 // Chapter 2. Finite-Dimensional Systems, pp. 13-104 // Chapter 3. Infinite Dimensional Systems, pp. 105-203 // Chapter 4. Time-Dependent Systems, pp. 205-230 // Index

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Fizika, Kemija



POVEZANOST RADA


Projekt / tema
098-0982915-2942 - Razvoj matematičkih metoda za opis strukture, dinamike i reaktivnosti molekula (Darko Babić, )

Ustanove
Institut "Ruđer Bošković", Zagreb

Profili:

Avatar Url Tomislav Živković (autor)

Citiraj ovu publikaciju

Živković, Tomislav P.
Exact Treatment of Finite-Dimensional and Infinite-Dimensional Quantum Systems, Hauppauge: Nova Science Publishers, 2010 (monografija)
Živković, T. (2010) Exact Treatment of Finite-Dimensional and Infinite-Dimensional Quantum Systems. Hauppauge, Nova Science Publishers.
@book{book, author = {\v{Z}ivkovi\'{c}, T.}, year = {2010}, pages = {230}, keywords = {local rank perturbation, exact treatment, quantum systems}, isbn = {978-1-61668-597-3}, title = {Exact Treatment of Finite-Dimensional and Infinite-Dimensional Quantum Systems}, keyword = {local rank perturbation, exact treatment, quantum systems}, publisher = {Nova Science Publishers}, publisherplace = {Hauppauge} }