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ADVANCED QUANTUM MECHANICS
Time: Fri BCD 9:00-12:00 Location: ED 201
Instructor: Oleksandr Voskoboynikov 霍斯科
Phone: 5712121 ext. 54174 Office: 646 ED bld.4 E-mail: [email protected] Office hours: by appointment Pre-requisite courses: Engineering Mathematics, Linear Algebra, Modern Physic, Electromagnetics Text book: J. J. Sakurai , Jim J. Napolitano, Modern Quantum Mechanics (2nd Edition), Addison-Wesley, 2011 (or any Edition) Reference books: 1. Daniel R. Bes, Quantum Mechanics (Second, Revised Edition), Springer, 2007 2. Franz Schwabl, Quantum Mechanics (Fourth Edition), Springer, 2007 3. Yehuda B. Band and Yshai Avishai, Quantum Mechanics with applications to nanotechnology and
information science, Elsevier, 2013 4. Class Notes. Credits: 3 (hours for weekly study –3) Grade: Home Works and Quiz 15% Midterm: 40% Final: 45%
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Complex Variables
Web: http://web.it.nctu.edu.tw/~vam/
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Course Description:
The course treats non-relativistic quantum mechanics. It
introduces foundations, principles and basic approaches of
quantum mechanics to experimental and theoretical exploration of
the nature. The course introduces techniques to solve quantum
mechanical problems. Some of the most important central force
problems including the theory of angular momentum and spin are
considered. Perturbation theory as well as other approximation
methods are discussed. Basic problems on atomic systems, multi-
particle systems, and quantum theory of scattering are considered.
In addition an introductory consideration is being given to the
quantum information processing.
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Introduction
Basic concepts of quantum mechanics
Wave functions, operators,
observables, and quantum measurement
1. Linear vector spaces. Hilbert space
2. Operators and representations
3. Wave function and density operator
4. Measurement, observables, uncertainty
relations
Evolutions of quantum systems
1.Time evolution and the Schrodinger equation
2.Schrodinger and Heisenberg pictures
3. Examples of solvable cases for the Schrodinger
equation
4. Propagators
5.Potentials and Gauge Transformations
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Theory of Angular Momentum 1.Rotation and angular momentum
2.Spin
3.Eigenvalues and eigenstates of angular
momentum operators
4. Schrodinger equation for central potentials
5. Addition of Angular Momenta
Approximation Methods 1. Time independent perturbation theory. Non-
degenerate and degenerate cases
2.Variational Methods
3.Hydrogenlike atoms. Fine structure and
Zeeman effect
4. The Wentzel-Kramers-Brillouin (WKB)
approximation
5.Time dependent perturbation theory
6.Interaction with the classical radiation fields.
Light emission and absorption
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Scattering Theory 1.The Lippmann-Schwinger Equation
2.The Born approximation
3.Optical theorem
4.Method of partial waves
5.Resonance scattering
Multi-practical Systems
1. Basic quantum statistics
2. Two-electron systems
3. The helium atom
4. The Hartree–Fock method
Elements of Quantum Information 1.Qubits’ concept
2.Quantum gates and elementary qubit operations
3. Quantum information processing. Physical
implementations
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“…trying to find a computer simulation of physics, seems
to me to be an excellent program to follow out … and I’m not happy with all the analyses that go with just
the classical theory, because
NATURE IST’T CLASSICAL,
dammit, and if you want to make a simulation of nature, you’d better
MAKE IT QUANTUM MECHANICAL,
and golly it’s a wonderful problem because it doesn’t look so easy.”
Richard Feynman (International Journal of Theoretical Physics, Vol.21,
p. 486, 1981)
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A FEW OF WELL KNOWN EXAMPLES:
#1. How does a magnet work?
People in ancient China discovered that natural lodestone magnets attracted iron. The
Chinese also found that a piece of lodestone would point in a north-south direction if it was
allowed to rotate freely. They used this characteristic of lodestone to tell fortunes and as a
guide for building. By A.D. 1200, sailors used magnetic compasses to steer their ships.
John H. Van Vleck of the United States and Louis E. F. Neel of France applied quantum
mechanics to understand the magnetic properties of atoms and molecules.
All magnets are macro-quantum objects
and
ħ 0 M, 0
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#2. How does the light work?
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#3. How does a superconductor work?
High Temperature
Ordinary Conductivity
At high temperature one observes
a state of ordinary conductivity
due to disorderly dynamics of the electrons
and a corresponding inner friction.
Low Temperature
Super-conductivity
At low temperature there is a unique
state of superconductivity
due to the coherent quantum
dynamics of the electrons with a
characteristic frictionless flow of the
electrons
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#4. How does a transistor work? (“To the electron -- may it never be of any use to anybody." JJ. Thomson's favorite toast)
What is a quasi-electron? Why has it “an effective mass”
What is a crystal ? What is a
semiconductor? The First Transistor (1947) The workbench of
John Bardeen and Walter Brattain at Bell Laboratories
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#5. What is a quantum computer?
Two-state bit can not compete a multi-state quantum bit
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0
.
.
.
n
Quantum bit Classical bit
1
0
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#6. How is designed the Universe?
The distribution of galaxies may help to confirm theories of quantum cosmology (NASA Picture )
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History
The electromagnetic radiation processed both a wave and a corpuscular
character. It’s energy is absorbed and emitted in separate portions – quanta-
photons
The photons momentum is determined by the vector
Where
1900 M. Plank 190 1905 A. Einstien
E2/h
Plank’s constant = 6.62x10-34Js
kp
ck
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1912 J. Frank and H. Hertz
The atomic energy states have a discrete character
(from the ionization potentials of gases)
1913 N. Bohr
The first successful attempt to explain the properties of the
hydrogen atom
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1924 L.de Broglie
A hypothesis of the wave properties of all particles of small mass
1926 E. Schrödinger
The Schrödinger's wave equation
vppk m ,
),,(),()(),(2
22
tt
itVtm
rrrr
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1927 C. J. Davison and G.P. Thomson
The experimental discovery of the diffraction of electrons by crystals
1926-1930 W. Heisenberg, P. Dirac, and W. Pauli
The discovery of new productive forms of the quantum theory
Quantum Mechanics
is now the basis of many new branches of the modern science
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From: Y. B. Band and Y. Avishai, Quantum Mechanics with applications to nanotechnology and information science.
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