Numerical Analysis (II)

數值分析

Spring 2006

HW5 (6/15): Hand in your term project in both doc (or tex) and pdf format.

HW4 (4/27): Hand in a preliminary report of your term project in both doc (or tex) and pdf format.

$\displaystyle Ax = \lambda x $HW3 (3/30): Write a program in C++ or Fortran for solving                   obtained by discretizing the Sturm-Liouville problem by FDM.

$\displaystyle Ax = \lambda x $HW2 (3/16): Derive                   from the Sturm-Liouville problem by FDM.

HW1 (3/16): Deduce the Schrodinger equation from scratch.

*Reading   **Programming   ***Home Work

I.                   Eigenvalue Problems

l           The general eigenvalue problem  (pdf*)

l           A Brief Tour of Eigenproblems

l           Matrix Transformation Methods

l           Templates for the Solution of Algebraic Eigenvalue Problems

1.      Power Method A (pdf*) Power Method B (pdf**)

2.      QR METHOD A (pdf*)

3.      Jacobi-Davidson Methods A (pdf*)  Jacobi-Davidson Methods B  (pdf*)

II.                Numerical Methods for PDEs

l          Poisson's equation 1  (pdf*)

l          Finite Difference Method (FDM) 1D  (pdf*)

l          Finite Element Method (FEM)   (pdf*)

l          Sturm-Liouville problem  (pdf*)

l          $\displaystyle Ax = \lambda x $Derive                        from the Sturm-Liouville problem by FDM. ***

III.             Quantum Mechanics

l          HyperPhysics

1.          What is the Schrodinger equation? (pdf*)

2.          Schrodinger Equation (pdf*)

3.          Free particle approach to the Schrodinger equation (pdf*)

4.          Traveling Wave (pdf*)

5.          DeBroglie Hypothesis (pdf*)

6.          Planck Hypothesis (pdf*)

7.          Wave-Particle Duality (pdf*)

8.          Operators in Quantum Mechanics (pdf*)

9.          Bra-ket notation (pdf*)

l          Hilbert space (pdf*)

l          Sobolev space (pdf*)

l          Linear operators (pdf*)

10.      Hamiltonian (pdf*)

11.      Postulates of Quantum Mechanics (pdf*)

12.      Expectation Value Postulate (pdf*)

13.      Schrodinger Equation II (pdf*)

14.      Solving 1D Schrodinger Equation (pdf***)

15.      Hydrogen Atom and Quantum Numbers (pdf***)

l          Spherical Polar Coordinates  (pdf)

l          The Radial Equation  (pdf)

l          The Colatitude Equation  (pdf)

l          The Azimuthal Equation  (pdf)

l          Hydrogen Wavefunctions  (pdf)

16.      Periodic Table (pdf*)  The Standard Model of particle physics

17.      Atomic Orbitals a  (pdf*) Atomic Orbitals b  (pdf*)

18.      Molecular Orbitals  (pdf*)

IV.              Hartree-Fock Molecular Orbital Theory

l          An Introduction to Hartree-Fock Molecular Orbital Theory

1.      What Problem Are We Solving?  (pdf*)

2.      Motivation and the Hartree Product (pdf*)

3.      Slater Determinants (pdf*)

4.      Simplified Notation for the Hamiltonian (pdf*)

5.      Energy Expression (pdf*)

6.      The Hartree-Fock Equations (pdf***)

7.      Lagrange multipliers (pdf***)

V.                 Semiconductor

VI.               Links

l          A history of computing

l          2020 Quantum Computers

l          Timeline of computing

l          History of mathematics

l          Timeline of quantum computing

 

 

Grading Policy: Projects and Home Works Only (100%).