Computational Physics
Simulation of Classical and Quantum Systems
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Beschreibung
This textbook presents basic numerical methods and applies them to a large variety of physical models in multiple computer experiments. Classical algorithms and more recent methods are explained. Partial differential equations are treated generally comparing important methods, and equations of motion are solved by a large number of simple as well as more sophisticated methods. Several modern algorithms for quantum wavepacket motion are compared. The first part of the book discusses the basic numerical methods, while the second part simulates classical and quantum systems. Simple but non-trivial examples from a broad range of physical topics offer readers insights into the numerical treatment but also the simulated problems. Rotational motion is studied in detail, as are simple quantum systems. A two-level system in an external field demonstrates elementary principles from quantum optics and simulation of a quantum bit. Principles of molecular dynamics are shown. Modern bounda
ry element methods are presented in addition to standard methods, and waves and diffusion processes are simulated comparing the stability and efficiency of different methods. A large number of computer experiments is provided, which can be tried out even by readers with no programming skills. Exercises in the applets complete the pedagogical treatment in the book. In the third edition Monte Carlo methods and random number generation have been updated taking recent developments into account. Krylov-space methods for eigenvalue problems are discussed in much more detail. The wavelet transformation method has been included as well as simple applications to continuum mechanics and convection-diffusion problems. Lastly, elementary quantum many-body problems demonstrate the application of variational and Monte-Carlo methods.Teaches basic numerical methods in theoretical physics
Features numerous computer examples, for which no programming skills are required
Provides detailed explanations without mathematical proofs
Discusses standard numerical methods as well as more recent developments
Includes problems and solutions
Teaches basic numerical methods in theoretical physics Features numerous computer examples, for which no programming skills are required Provides detailed explanations without mathematical proofs Discusses standard numerical methods as well as more recent developments Includes problems and solutions Includes supplementary material: sn.pub/extras
Autor*in
Philipp O.J. Scherer
Themen in »Computational Physics«
Understanding Computer Simulation Inhomogeneous Linear Equations Simulation of Classical and Quantum Systems Teacher Simulation Methods Textbook on Computational Physics Textbook on Numerical Methods