Ebook: Numerical Quantum Dynamics

It is an indisputable fact that computational physics form part of the essential landscape of physical science and physical education. When writing such a book, one is faced with numerous decisions, e. g. : Which topics should be included? What should be assumed about the readers’ prior knowledge? How should balance be achieved between numerical theory and physical application? This book is not elementary. The reader should have a background in qu- tum physics and computing. On the other way the topics discussed are not addressed to the specialist. This work bridges hopefully the gap between - vanced students, graduates and researchers looking for computational ideas beyond their fence and the specialist working on a special topic. Many imp- tant topics and applications are not considered in this book. The selection is of course a personal one and by no way exhaustive and the material presented obviously reflects my own interest. What is Computational Physics? During the past two decades computational physics became the third fun- mental physical discipline. Like the ‘traditional partners’ experimental physics and theoretical physics, computational physics is not restricted to a special area, e. g. , atomic physics or solid state physics. Computational physics is a meth- ical ansatz useful in all subareas and not necessarily restricted to physics. Of course this methods are related to computational aspects, which means nume- cal and algebraic methods, but also the interpretation and visualization of huge amounts of data.

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This book describes computational methods used in quantum dynamics with emphasis on small quantum systems. Computational physics is a fundamental physical discipline at the forefront of physical research. Thus it is an indisputable fact that computational physics form part of the essential landscape of physical science and education. In the present state of scientific knowledge the importance of quantum dynamics is commonplace. Computational quantum dynamics involves the use of computer calculations and simulations to solve quantum physical problems. Following a brief introduction to quantum dynamics the book revisits approximation techniques based on perturbational theory and variationalmethods. This discussion includes Hartree-Fock and density functional theory and quantum Monte Carlo methods. The next chapter presents the concepts of finite differences. Central in this chapter is the discretization in time and space. Later chapters concentrate on discrete variable techniques based on orthogonal polynomials, finite element and B-splinemethods for both time-independent and time-dependent problems and the combination of different computational techniques. The final chapter contains a list of useful sources for computational software and program codes. This book is primarily aimed at advanced students and graduates and researchers in theoretical and computational physics or chemistry and bridges the gap between quantum textbooks and computational research. Although not essential, the reader should have a basic background in quantum physics and some knowledge of numerical analysis would be helpful in reading this book.