Computational Quantum Mechanics
Spring 2005

Numerical Methods

• Lecture Notes: 
  
  1. J.-L. Liu, Numerical Methods for Partial Differential Equations (available by request).
  2. J.-L. Liu, 1D Finite Element Method, 2D Finite Element Method.
  3. J.-L. Liu and J.-H. Chen, Jacobi-Davidson Method.
  
  
• Book [BF01]: R. L. Burden and J. D. Faires, Numerical Analysis, Brooks/Cole, 2001.
  
  Reading: 
  1. Conjugate Gradient Method [p. 465]
  2. Power Method [p. 560]
  3. QR Algorithm [p. 585]
  4. Newton's Method, Quasi-Newton Methods, Broyden's Method [p. 611]
  5. Finite Element Method [p. 726]
• Book [ZT89]: Zienkiewicz and Taylor, The Finite Element Method  ,4th ed, McGraw-Hill,1989.
  
  Reading: 
  1. 3D Gaussian Quadrature
  2. 3D Finite Element Shape Functions in Volume Coordinates

Quantum Mechanics

• Book [G92]: A. Goswami, Quantum Mechanics, Wm. C. Brown Publisher, 1992.
  
  Reading: 
  1. Schrodinger's Eq. [p. 12]
  2. Hamiltonian Operator [p. 54]
  3. Solution of 1D Schrodinger Eq. [p. 71]
  4. Dirac's Description of QM [p. 112]
  5. Two-Particle System: Exchange [p. 184], Correlation [p. 186], Symmetry, Antisymmetry, Fermions, Bosons
  6. Central-Field Hamiltonian, Radial Eq., Quantum Number |nlm>, s, p, d, f orbitals [p. 237]
  7. Hydrogen Atom [p. 256]
  8. Helium Atom [p. 388]
  9. Hartree's Eq.: Variational Functional, Trial Wave Function, Lagrange Multipliers [p. 400]
  10. Periodic Table [p. 404]
  11. Quantum Systems: Atoms and Molecules, Molecular Structure, Molecular Orbitals [p. 399]
• Lecture Notes: 
  J.-L. Liu, Computational Quantum Mechanics 1, 2, 3.

Density Functional Theory

• Tutorials: Arias (Reading), 
• Lecture Notes: Cuevas, Beck, Saad, 江進福, 許正餘, 李明憲

Semiconductor Nano-Structures

• Lecture Notes:
  1. J.-L. Liu, Lecture 1: Poisson's Equation, Drift-Diffusion Equation, Boltzmann's Equation.
  2. J.-L. Liu, Lecture 2: Numerical Simulations of Semiconductor Nanostructures.
• Papers:
  1. R.-C. Chen and J.-L. Liu, A quantum corrected energy-transport model for nanoscale semiconductor devices, J. Comp. Phys., 204 (2005), pp. 131-156.

Assignments

1. (Due 3/21) Numerical results of H, He, and Li.
2. (Due 4/11) Numerical results of H2+.