Instructor: Bernardo Barbiellini

Office: Dana 136

Phone: 373 2961

Email:bba@neu.edu

Lectures

Texts

• Introduction to Computer Simulation Methods: Applications to Physical Systems
  by Harvey Gould and Jan Tobochnik
• Computational Physics by Tao Pang

Office Hours

Course Description

This course gives a modern introduction to the basic methods in computational physics and an overview of the recent progress in scientific computing. Many examples from recent research in physics and related areas are given with the fortran program listing. Basic computational tools and routines, including the ones for differential equations, spectral analysis, and matrix operations, are dealt with through relevant examples, and more advanced topics, such as Monte Carlo simulations, molecular dynamics, and quantum computing are also treated.

General Topics to be Covered

1. Basic Mathematical Operations
   1. Review of Fortran and accuracy considerations
   2. Interpolations, differentiation and integration
   3. Random numbers generators
2. Numerical methods for matrices
   1. Linear Algebra (systems of linear equations, Gaussian elimination)
   2. Eigenvalues and Eigenvectors
   3. Spectral Methods and Fast Fourier Transform
3. Variational Principle and Minimization
   1. Extremes of a multivariable function (Newton method, steepest descents, conjugate gradients)
   2. The Ritz variational method and Eigenvalue problems
   3. Inverse problem (Maximun entropy method)
4. Ordinary Differential Equations (ODE)
   1. Newton's Law of motion and Molecular dynamics (Verlet algorithm)
   2. Chaotic systems
   3. Schroedinger equation (Numerov algorithm)
   4. Electronic structure of atoms (Hartree-Fock approximation and Density Functional Theory)
5. Stochastic Methods
   1. Metropolis algorithm
   2. Variational Quantum Monte Carlo
   3. The Stochastic Gradient Approximation (Robbins and Monro Theorem)
   4. Electronic structure of molecules
6. Partial Differential Equations (PDE)
   1. Maxwell's Equations in Matter and Ising ferromagnet
   2. Diffusion Quantum Monte Carlo.
7. High-performance computing
   1. Parallel computing (MPI)
   2. Quantum computing

• Stardec (ASCC)
• Fortran 90
• Simulations in Physics (Harvey Gould)
• Computational Physics (Tao Pang)
• Quantum Computing
• Secure Shell (ssh) for NT machines (self-extracting zip file)

The grade will be based on assigned projects and quizzes.