Numerical quantum dynamics (Q2784575)

It is an indisputable fact that computational physics has become one of the fundamental disciplines in physical science. In this book the author concentrates on numerical quantum methods adequate mainly for small computer systems.NEWLINENEWLINENEWLINEThe book consists of eight chapters. Chapter 1 formalizes some of the ideas of quantum mechanics and introduces the notation used throughout the book. The Dirac description is briefly discussed; angular momentum, the Euler angles and the Wigner rotation function are introduced. The motion of wave packets and some comments about the discretization of the time propagator can also be found here. Chapter 2 is devoted to the discussion of integrability and separability, contains a list of all coordinate systems for which the three-dimensional Schrödinger equation could be separable.NEWLINENEWLINENEWLINEChapters 3 and 4 revisit approximation techniques. Starting with Schrödinger perturbation theory other topics covered are Rayleigh-Ritz variational principle, linear algebra routines, Hartree-Fock and density functional theory, virial theorem and quantum Monte Carlo methods.NEWLINENEWLINENEWLINEChapter 5 contains finite differences and initial value problems for ordinary differential equations. Central in this chapter is the discretization of the uni-dimensional time-dependent Schrödinger equation in the space and time variable.NEWLINENEWLINENEWLINEThe theory of discrete variables is the subject of Chapter 6. Orthogonal polynomials are discussed and the computation of their nodes are explained. Chapter 7 is devoted to the discussion of finite elements. The final chapter contains a list of useful sources for software.NEWLINENEWLINENEWLINEThe book is very useful to graduate students and researchers who look for computational methods in quantum dynamics.