1.

Record Nr.

UNINA9910480338603321

Autore

Jirari Alouf <1965->

Titolo

Second-order Sturm-Liouville difference equations and orthogonal polynomials / / Alouf Jirari

Pubbl/distr/stampa

Providence, Rhode Island : , : American Mathematical Society, , 1995

©1995

ISBN

1-4704-0121-5

Descrizione fisica

1 online resource (154 p.)

Collana

Memoirs of the American Mathematical Society, , 0065-9266 ; ; Number 542

Disciplina

515/.625

Soggetti

Sturm-Liouville equation

Difference equations

Orthogonal polynomials

Electronic books.

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

"January 1995, Volume 113, Number 542 (second of 4 numbers)."

Nota di bibliografia

Includes bibliographical references.

Nota di contenuto

""Table of Contents""; ""List of Figures""; ""Acknowledgements""; ""Chapter 1. Introduction""; ""1.1 The Vibrating String""; ""1.2 Network Theory""; ""1.3 Random Walk With Discrete Time Process""; ""Chapter 2. Regular Sturm-Liouville Problem""; ""2.1 Set Up""; ""2.2 Preliminary Results""; ""2.3 Orthogonality, Eigenfunction Expansion, Spectral Function, and Green's Function""; ""Chapter 3. Singular Sturm-Liouville Problem""; ""3.1 Definition""; ""3.2 C[sub(b')] Circles""; ""3.3 C[sub(a')] Circles""; ""3.4 Existence of Boundary Conditions""; ""3.5 Singular Boundary Value Problems""

""3.6 Green's Function""""3.7 Self-Adjointness""; ""3.8 λ-Independence of Boundary Conditions""; ""3.9 Green's Formulas""; ""3.10 Spectral Resolution""; ""3.11 Limit-Point and Limit-Circle Tests""; ""Chapter 4. Polynomial Solutions""; ""4.1 Formal Self-Adjointness""; ""4.2 Polynomial Solutions""; ""4.3 Orthogonality of Eigenfunctions""; ""4.4 Eigenfunction Expansion""; ""Chapter 5. Polynomial Examples""; ""5.1 Classification""; ""5.2 Recurrence Relations""; ""5.3 Weight Functions and Self-Adjoint Forms""; ""5.4 Orthogonality""; ""5.5 Evaluation of the ||.||[sup(2)]""; ""5.6 Zeros""



""Chapter 6. The Four Representative Examples""""6.1 The Generalized Tchebyshev Polynomials""; ""6.2 The Generalized Laguerre Polynomials""; ""6.3 The Krawtchouk Polynomials""; ""6.4 The Charlier Polynomials""; ""Chapter 7. Left-Definite Spaces""; ""7.1 Finite Intervals""; ""7.2 Infinite Intervals""; ""References""

2.

Record Nr.

UNINA9910146623603321

Titolo

Mathematical Physics of Quantum Mechanics : Selected and Refereed Lectures from QMath9 / / edited by Joachim Asch, Alain Joye

Pubbl/distr/stampa

Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2006

ISBN

9786610627066

9781280627064

1280627069

9783540342731

3540342737

Edizione

[1st ed. 2006.]

Descrizione fisica

1 online resource (490 p.)

Collana

Lecture Notes in Physics, , 1616-6361 ; ; 690

Disciplina

530.120151

Soggetti

Mathematical physics

Quantum theory

Mathematical analysis

Mathematical Methods in Physics

Quantum Physics

Analysis

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographic references and index.

Nota di contenuto

Quantum Dynamics and Spectral Theory -- Solving the Ten Martini Problem -- Swimming Lessons for Microbots -- Landau-Zener Formulae from Adiabatic Transition Histories -- Scattering Theory of Dynamic Electrical Transport -- The Landauer-Büttiker Formula and Resonant Quantum Transport -- Point Interaction Polygons: An Isoperimetric Problem -- Limit Cycles in Quantum Mechanics -- Cantor Spectrum for Quasi-Periodic Schrödinger Operators -- Quantum Field



Theory and Statistical Mechanics -- Adiabatic Theorems and Reversible Isothermal Processes -- Quantum Massless Field in 1+1 Dimensions -- Stability of Multi-Phase Equilibria -- Ordering of Energy Levels in Heisenberg Models and Applications -- Interacting Fermions in 2 Dimensions -- On the Essential Spectrum of the Translation Invariant Nelson Model -- Quantum Kinetics and Bose-Einstein Condensation -- Bose-Einstein Condensation as a Quantum Phase Transition in an Optical Lattice -- Long Time Behaviour to the Schrödinger–Poisson–X? Systems -- Towards the Quantum Brownian Motion -- Bose-Einstein Condensation and Superradiance -- Derivation of the Gross-Pitaevskii Hierarchy -- Towards a Microscopic Derivation of the Phonon Boltzmann Equation -- Disordered Systems and Random Operators -- On the Quantization of Hall Currents in Presence of Disorder -- Equality of the Bulk and Edge Hall Conductances in 2D -- Generic Subsets in Spaces of Measures and Singular Continuous Spectrum -- Low Density Expansion for Lyapunov Exponents -- Poisson Statistics for the Largest Eigenvalues in Random Matrix Ensembles -- Semiclassical Analysis and Quantum Chaos -- Recent Results on Quantum Map Eigenstates -- Level Repulsion and Spectral Type for One-Dimensional Adiabatic Quasi-Periodic Schrödinger Operators -- Low Lying Eigenvalues of Witten Laplacians and Metastability(After Hel.er-Klein-Nier and Helffer-Nier) -- The Mathematical Formalism of a Particle in a Magnetic Field -- Fractal Weyl Law for Open Chaotic Maps -- Spectral Shift Function for Magnetic Schrödinger Operators -- Counting String/M Vacua.

Sommario/riassunto

At the QMath9 meeting, young scientists learn about the state of the art in the mathematical physics of quantum systems. Based on that event, this book offers a selection of outstanding articles written in pedagogical style comprising six sections which cover new techniques and recent results on spectral theory, statistical mechanics, Bose-Einstein condensation, random operators, magnetic Schrödinger operators and much more. For postgraduate students, Mathematical Physics of Quantum Systems serves as a useful introduction to the research literature. For more expert researchers, this book will be a concise and modern source of reference.