Quantum Mechanics Using Computer Algebra

Introductory text for graduate students in physics taking a year-long course in quantum mechanics in which the third quarter is devoted to relativistic wave equations and field theory. Answers to sele

Quantum networks build on entanglement and quantum measurement to achieve tasks that are beyond the reach of classical systems. Using quantum effects, we can detect the presence of eavesdroppers, rais

The third edition of this classic graduate-level physics text covers relativistic quantum mechanics, field quantization, causal perturbation theory, properties of the S-matrix, and considerations of o

A mind-blowing glimpse into the near future, where quantum computing will have world-transforming effects.The quantum computer is no longer the stuff of science fiction. Pioneering physicists are on t

Quirky Quantum Concepts explains the more important and more difficult concepts in theoretical quantum mechanics, especially those which are consistently neglected or confusing in many common expositi

Quantum and Classical Connections in Modeling Atomic, Molecular and Electrodynamic Systems is intended for scientists and graduate students interested in the foundations of quantum mechanics and appli

This book constitutes the refereed proceedings of the 5th International Conference on Algebra and Coalgebra in Computer Science, CALCO 2013, held in Warsaw, Poland, in September 2013. The 18 full pape

Traditionally, philosophers of quantum mechanics have addressed exceedingly simple systems: a pair of electrons in an entangled state, or an atom and a cat in Dr. Schrodinger's diabolical device. But

This book presents the conceptual framework underlying the atomistic theory of matter, emphasizing those aspects that relate to current flow. This includes some of the most advanced concepts of non-equilibrium quantum statistical mechanics. No prior acquaintance with quantum mechanics is assumed. Chapter 1 provides a description of quantum transport in elementary terms accessible to a beginner. The book then works its way from hydrogen to nanostructures, with extensive coverage of current flow. The final chapter summarizes the equations for quantum transport with illustrative examples showing how conductors evolve from the atomic to the ohmic regime as they get larger. Many numerical examples are used to provide concrete illustrations and the corresponding Matlab codes can be downloaded from the web. Videostreamed lectures, keyed to specific sections of the book, are also available through the web. This book is primarily aimed at senior and graduate students.

Assessment is a key driver in mathematics education. This book examines computer aided assessment (CAA) of mathematics in which computer algebra systems (CAS) are used to establish the mathematical pr

This book is intended for the undergraduate one or two semester course in modern algebra, also called abstract algebra. It follows that basic plan, using the axioms or rules to understand structures s

The open research center project “Interdisciplinary fundamental research toward realization of a quantum computer” has been supported by the Ministry of Education, Japan for five years. This is a coll

In the last decade many important advances have taken place in the field of quantum optics, with numerous potential applications. Ideal for graduate courses on quantum optics, this textbook provides an up-to-date account of the basic principles of the subject. Focusing on applications of quantum optics, the textbook covers recent developments such as engineering of quantum states, quantum optics on a chip, nano-mechanical mirrors, quantum entanglement, quantum metrology, spin squeezing, control of decoherence and many other key topics. Readers are guided through the principles of quantum optics and their uses in a wide variety of areas including quantum information science and quantum mechanics. The textbook features end-of-chapter exercises with solutions available for instructors at www.cambridge.org/9781107006409. It is invaluable to both graduate students and researchers in physics and photonics, quantum information science and quantum communications.

The author defines “Geometric Algebra Computing” as the geometrically intuitive development of algorithms using geometric algebra with a focus on their efficient implementation, and the goal of this b

Quantum cryptography (or quantum key distribution) is a state-of-the-art technique that exploits properties of quantum mechanics to guarantee the secure exchange of secret keys. This 2006 text introduces the principles and techniques of quantum cryptography, setting it in the wider context of cryptography and security, with specific focus on secret-key distillation. The book starts with an overview chapter, progressing to classical cryptography, information theory (classical and quantum), and applications of quantum cryptography. The discussion moves to secret-key distillation, privacy amplification and reconciliation techniques, concluding with the security principles of quantum cryptography. The author explains the physical implementation and security of these systems, enabling engineers to gauge the suitability of quantum cryptography for securing transmission in their particular application. With its blend of fundamental theory, implementation techniques, and details of recent prot

This book constitutes the proceedings of the 14th International Workshop on Computer Algebra in Scientific Computing, CASC 2012, held in Maribor, Slovenia, in September 2012. The 28 full papers presen

The present book provides to the main ideas and techniques of the rapid progressing field of quantum information and quantum computation using isotope - mixed materials. It starts with an introduction

This book deals with several topics in algebra useful for computer science applications and the symbolic treatment of algebraic problems, pointing out and discussing their algorithmic nature. The topi

Combining physics, mathematics and computer science, topological quantum computation is a rapidly expanding research area focused on the exploration of quantum evolutions that are immune to errors. In this book, the author presents a variety of different topics developed together for the first time, forming an excellent introduction to topological quantum computation. The makings of anyonic systems, their properties and their computational power are presented in a pedagogical way. Relevant calculations are fully explained, and numerous worked examples and exercises support and aid understanding. Special emphasis is given to the motivation and physical intuition behind every mathematical concept. Demystifying difficult topics by using accessible language, this book has broad appeal and is ideal for graduate students and researchers from various disciplines who want to get into this new and exciting research field.

Perhaps the greatest physicist of the second half of the twentieth century, Richard Feynman changed the way we think about quantum mechanics, the most perplexing of all physical theories. Here Lawrenc

Starting from first principles, this book introduces the fundamental concepts and methods of dissipative quantum mechanics and explores related phenomena in condensed matter systems. Major experimenta

Build an intuitive understanding of the principles behind quantum mechanics through practical construction and replication of original experimentsWith easy-to-acquire, low-cost materials and basic kno

Thermodynamics has benefited from nearly 100 years of parallel development with quantum mechanics. As a result, thermal physics has been considerably enriched in concepts, technique and purpose, and now has a dominant role in the developments of physics, chemistry and biology. This unique book explores the meaning and application of these developments using quantum theory as the starting point. The book links thermal physics and quantum mechanics in a natural way. Concepts are combined with interesting examples, and entire chapters are dedicated to applying the principles to familiar, practical and unusual situations. Together with end-of-chapter exercises, this book gives advanced undergraduate and graduate students a modern perception and appreciation for this remarkable subject.

During the past 15 years, quantum field theory and classical statistical mechanics have merged into a single field, and the need for nonperturbative methods for the description of critical phenomena i

This is the first book of its kind which teaches matrix algebra, allowing the student to learn the material by actually working with matrix objects in modern computer environment of R. Instead of a ca

A Polynomial Approach to Linear Algebra is a text which is heavily biased towards functional methods. In using the shift operator as a central object, it makes linear algebra a perfect introduction to

A highly entertaining exploration of the complicated science of quantum mechanics made easy to understand by way of pop culture. As a young science fiction fan, physicist James Kakalios marveled at

Differential geometry is the study of the curvature and calculus of curves and surfaces. A New Approach to Differential Geometry using Clifford's Geometric Algebra simplifies the discussion to an acce

A Novel Pedagogical Approach to Quantum Mechanics"A physical understanding is a completely unmathematical, imprecise, and inexact thing, but absolutely necessary for a physicist." —R. FeynmanThe

Motivated by the importance of the Campbell, Baker, Hausdorff, Dynkin Theorem in many different branches of Mathematics and Physics (Lie group-Lie algebra theory, linear PDEs, Quantum and Statistical

Quantum computing and quantum information are two of the fastest growing and most exciting research fields in physics. Entanglement, teleportation and the possibility of using the non-local behavior o

In trying to understand the atom, physicists built quantum mechanics, the most successful theory in science and the basis of one-third of our economy. They found, to their embarrassment, that with th

Traditionally, philosophers of quantum mechanics have addressed exceedingly simple systems: a pair of electrons in an entangled state, or an atom and a cat in Dr. Schrodinger's diabolical device. But

The combination of two of the twentieth century's most influential and revolutionaryscientific theories, information theory and quantum mechanics, gave rise to a radically new view ofcomputing and inf

A new discipline, Quantum Information Science, has emerged in the last two decades of the twentieth century at the intersection of Physics, Mathematics, and Computer Science. Quantum Information Proce

The application of quantum mechanics to many-particle systems has been an active area of research in recent years as researchers have looked for ways to tackle difficult problems in this area. The qua

This book is the first of a series covering the major topics that are taught in university courses in Theoretical Physics: Mechanics, Electrodynamics, Quantum Theory and Statistical Physics.

Engineers and scientists need to have an introduction to the basics of linear algebra in a context they understand. Computer algebra systems make the manipulation of matrices and the determination of

An accessible introduction to the theoretical and computational aspects of linear algebra using MapleTMMany topics in linear algebra can be computationally intensive, and software programs often serve

This 2004 textbook provides a pedagogical introduction to the formalism, foundations and applications of quantum mechanics. Part I covers the basic material which is necessary to understand the transition from classical to wave mechanics. Topics include classical dynamics, with emphasis on canonical transformations and the Hamilton-Jacobi equation, the Cauchy problem for the wave equation, Helmholtz equation and eikonal approximation, introduction to spin, perturbation theory and scattering theory. The Weyl quantization is presented in Part II, along with the postulates of quantum mechanics. Part III is devoted to topics such as statistical mechanics and black-body radiation, Lagrangian and phase-space formulations of quantum mechanics, and the Dirac equation. This book is intended for use as a textbook for beginning graduate and advanced undergraduate courses. It is self-contained and includes problems to aid the reader's understanding.