This book provides a physical introduction to the finite element method through the discretization of the action integral. Being a variational approach, the finite element method provides the means for systematically improving accuracy in a natural manner. The action and variational principles are shown to provide means for adaptively improving results in FEM. The method is applied to quantum mechanical problems in a number of areas, such as atomic physics, physics of quantum semiconductor structures and electron transport in mesoscopic structures. The finite element method applied to quantum heterostructures has led to the paradigm of wavefunction engineering using which heterostructures have been successfully designed for opto-electronic applications--the design of the Quantum Interband Cascade laser is described. The finite element method is applied to the solution of nonlinear Schrödinger equations such as the Ginzburg-Landau equation in superconductivity.

The Green's function approach to the boundary integral relation, together with its discretization leading to the boundary element method, is presented from fundamentals The method is applied to the calculation of electric field enhancements at metallic surfaces due to surface plasmon excitations, to quantum mechanical scattering, and to quantum waveguides.

The material is aimed at senior undergraduates, graduate students, and those interested in computational methods and their applications to physical problems.

• This is an impressive manuscript of a book, which is bound to open new ground for future aspiring physicists, particularly those interested in condensed matter physics and chemistry. The book has eighteen Chapters broken into five parts with a sixth part containing three Appendices giving details of special topics of constant use in the development of this book. The author has done a marvelous job of doing all this in only ~600 pages! The book covers a lot of ground in modern quantum mechanical description of condensed matter. It is a unified and careful exposition of Finite Element and Boundary Element methods applied to a large corpus of problems from simple quantum systems to quantum waveguides including time-dependent applications. Thus the author has rightfully introduced the reader to the new field of "wave-function engineering.." The treatment of Schrödinger - Poisson equations that are the first set of self-consistent equations to be solved in condensed matter problems is very well done. The author includes treatment of realistic systems under the influence of external fields, in various geometric configurations, etc., all of which are very important. Finally, he has an important chapter on time-dependent problems, which are only being examined seriously in recent times. Here he brings together different approaches from disparate fields under the aegis of solving the equations that arise as one single stationary action principle and presents a clear picture of what is involved in solving the time-dependent problems in contrast to stationary problems. My overall impression of this book is that it is going to be an important textbook for senior undergraduates, graduate students, as well as research workers whether they are advanced or beginning their career. The book has many gems in it not often spelled out in textbooks and is very current in its approach because it combines neatly the analytical and computational aspects. It contains references to a very large body of literature, which adds to the usefulness of the book for advanced research workers. I believe that the author by writing this book has made the methods of Finite Element and Boundary Element as methods of choice in condensed matter physics and chemistry!
• The book is generally well structured and remarkably comprehensive. Particularly nice to see was the inclusion of a chapter on sparse matrix methods -- critical to the practical implementation of finite-element methods and all too often neglected. A chapter was (quite rightly) devoted to atomic systems. The book is well written and fills a significant gap in the literature. I would wholeheartedly recommend it to students and colleagues alike.
• The book is well organized, and it covers an excellent selection of very good topics. Solution of Schrödinger equation, self-consistent model including Poisson equation, effects of magnetic field, and design of mid-IR type-II quantum-well lasers are excellent topics and state-of-the art research topics, on which the author has personally made a significant contribution that have been recognized. The 2D applications of FEM and Part V on BEM are all very useful. I am glad to see that the author is able to put all these subjects together in a compact textbook. The book is clear to follow for senior undergraduate, graduate students and researchers in the field. The style of presentation is professional.