Green’s Functions in Quantum Physics (Springer Series in Solid-State Sciences, 7) 3rd Edition by Eleftherios N. Economou | (PDF) Free Download

Description

This book will be of interest to advanced students wishing to become familiar with the method of Green’s functions for obtaining simple and general solutions to basic problems in quantum physics.

User’s Reviews

Editorial Reviews: Review From the reviews of the third edition:”The main purpose of this book is to provide graduate students, and also experienced researchers, with a clear and quite detailed survey of the applications of Green’s functions in different modern fields of quantum physics. … In summary, this book is a good manual for people who want to understand the physics and the various applications of Green’s functions in modern fields of physics. It can also be used as a starting point for studying numerical analysis in condensed matter theory.” (Jean-Yves-Fortin, Mathematical Reviews, Issue, 2007 i) From the Back Cover The main part of this book is devoted to the simplest kind of Green’s functions, namely the solutions of linear differential equations with a -function source. It is shown that these familiar Green’s functions are a powerful tool for obtaining relatively simple and general solutions of basic problems such as scattering and bound-level information. The bound-level treatment gives a clear physical understanding of “difficult” questions such as superconductivity, the Kondo effect, and, to a lesser degree, disorder-induced localization. The more advanced subject of many-body Green’s functions is presented in the last part of the book.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐If you want to know about the Dirac Notation or the quantum applications for Green’s function, well then you’re out of luck. But if you want to know the math of Green’s function or maybe you’re hoping on understanding what Green’s function is all about then it’s a good book to get. It will give you many clear cut (i.e. with Green’s function on the left side of the equation and a function on the right side of the equation) examples of Green’s function without it being tied up in a convolution as a kernel. However Green’s function has not been given a single master algebraic formula irrespective of it conditions. I give it only two stars because I’m a tough grader; in order for a book to be given a five stars rating by me, it would need to explain every single notation, symbol, variable, and index with illustrations, also any application would have to be clear as well.

⭐This book is essential to any theorist working in solid state/condensed matter physics. It’s the most complete treatment of how to use these wonderful mathematical objects to get solutions. One of it’s greatest accomplishments though is how it cuts through the decades of confusing names and notation concerning the use of Green functions in condensed matter. Ever wonder how the scattering matrix is related to the Green function formalism? Why the eigenvalues of tight binding hamiltonian look so much like those of a harmonic oscillator? This is a great book.

⭐This is a helpful book for understanding what the physical content of a Green function is (which is a lot). In quantum mechanics, a Green function is an in-general time-dependent amplitude for the overlap between an initial and final state; in quantum statistical mechanics (the underlying machinery of condensed matter physics), it is a time-dependent ensemble-average. In both, observables are built of these abovementioned amplitudes and ensemble average. The formalism of Green functions is highly abstract and a great deal of physicality is often concealed in subtleties (e.g., branch-cuts, poles, etc.), but this book provides insight into these; this insight becomes valuable when one is writing results of research and consequently wishes to speak precisely and without error. Solutions to problems are included, making this useable for self-study.

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