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.
HW3 (3/30): Write a program in
C++ or Fortran for solving
obtained by discretizing the Sturm-Liouville problem by FDM.
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
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The general eigenvalue problem
(pdf*)
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A Brief Tour of
Eigenproblems
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Matrix Transformation Methods
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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
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Poisson's
equation 1 (pdf*)
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Finite
Difference Method (FDM) 1D (pdf*)
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Finite Element Method
(FEM) (pdf*)
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Sturm-Liouville
problem (pdf*)
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Derive
from the Sturm-Liouville problem by FDM. ***
III.
Quantum Mechanics
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*)
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Hilbert
space (pdf*)
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Sobolev
space (pdf*)
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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***)
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Spherical
Polar Coordinates (pdf)
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The
Colatitude Equation (pdf)
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The
Azimuthal Equation (pdf)
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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
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An Introduction
to Hartree-Fock Molecular Orbital Theory
1.
What Problem Are We Solving?
(pdf*)
2.
Motivation and the Hartree Product (pdf*)
4.
Simplified Notation for the Hamiltonian (pdf*)
6.
The Hartree-Fock Equations (pdf***)
7.
Lagrange multipliers (pdf***)
V.
Semiconductor
VI.
Links
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Timeline of
quantum computing
Grading Policy:
Projects and Home Works Only (100%).