Semiclassical Physics 1st Edition by Matthias Brack (PDF)

Description

This book attempts to convey to the reader that semiclassical physics can be fun, as well as useful for understanding quantum fluctuations in interacting many-body systems. It presents applications to finite fermion systems in diverse areas of physics.

User’s Reviews

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

⭐A pity this textbook is not better known ! Here is the publisher’s blurb: “The approach is informal, guided largely by simple solvable models and by practical applications to real physical phenomena.” Happily, that is true ! In any event, inspired by Gutzwiller’s 1990 exegesis, Chaos in Classical and Quantum Mechanics, I desired for more. That is, more detail, more applications. This textbook fits the bill beautifully. Whereas Gutzwiller is to be utilized for inspiration, Brack and Bhaduri is to be sought after for more explication.(1) There are exercises for the student. In fact, the selection of exercises is outstanding. Many–if not, most–are multi-step problems which lead the student by the hand to a solution. Not only is that a positive pedagogic and strategic attribute, these exercises are simply fun to read ! An example of the strategy: “Prove equation #7.151 for the Green’s function of the annular billiard.” The hints for solution are helpful: start with equation #7.142, take advantage of circular symmetry… make the expansion… expand the Dirac delta function…hence find the radial equation… apply the boundary condition…” (page 357). And, so it goes. Each exercise replete with hints to assist in a solution. Excellent !(2) More pedagogy: “many examples, often solving the same model by different techniques at different places in the book.” (preface). The authors provide a roadmap, of sorts: Easier chapters (1, 2, and 8), then “core material” (4 & 5) and finally extensions of theory (6 and 7). So it is. Chapters one and two will (or should) be easier to assimilate. The book deals only with non-relativistic problems (page 4). First chapter introduces Feynman path integral. Read: “one may well ask if classical dynamics, and chaos in particular, have some effect on the wave function.” (page 39).Then, read of asymmetric fission of an atomic nucleus–the topic will reappear later in the text (chapter eight).(3) Bibliographic references, as well as student exercises, concludes each chapter. Appendix C is useful: a synopsis of linear differential equations with periodic coefficients. Chapter three presents synopsis of “basic quantum mechanical tools needed to calculate the density-of-states.” (page 111, pay attention to how spin is introduced into the formalism of the text. That is, read the paragraph on page 117). Harmonic oscillator features prominently throughout the textbook. While the book is challenging, where it is challenging it is also pedagogic. Example: Glancing at page 131 (“for the calculations below…”), you are asked to supply derivations. The authors walk you through the steps: rewrite summations, use the identity, use Gaussian integral, etc. Thus, while the book is not necessarily easy, it is necessarily helpful. Problem #3.4 introduces Anyons, a six-part excursion (page 138).(4) Another focus: Gutzwiller trace formula, which “we have taken care… to derive from an elementary level.” Chapter five does just that: ” we derive Gutzwiller’s trace formula for isolated orbits, going into quite some detail.” Read: “although mathematically trivial, the successful analytical application of the trace formula to these systems does not appear to be common knowledge.” (page 229). Also, a look at the Wigner distribution function (chapter four) along with its use for Husimi transform (problem #4.1). Mathematics will be helpful, too: Section #4.5.1 will expound upon the Euler-MacLaurin expansion (pages 177-180). As for extensions, in chapter six, read: “in this chapter one always makes the assumption that only periodic orbits are important.” (page 246).(5) As with Gutzwiller (monograph,1990), this textbook is an astute mixture of physics and mathematics. For instance, you are introduced to Riemann-Zeta function (pages 298-301). Following which, the Selberg Zeta function (page 308). Matrices, Green’s functions, Hankel functions, determinants, all these and more will be utilized. The book concludes: “a creature living on a two-dimensional flat space of a three-dimensional classical system, seems to witness quantum-like behavior. Individual events hit at random, but a regular pattern may emerge after many hits. Reminiscent are the quantal hits of a self-interfering photon or electron from the famous double slit experiment. Is there a hint here that there may be a connection between dimensional reduction and quantum effects.” (page 404).(6) Concluding my assessment: If perusal of Gutzwiller leaves you wanting for more, then look no further !This textbook is an excellent companion to Gutzwiller. But, it is much more than that !This text leads you by the hand and employs pedagogic strategies to maximize learning the material.The efficacy of this textbook can hardly be overstated. It is one of my favorites.

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