ADVANCED QUANTUM MECHANICS

Transcription

1 ADVANCED QUANTUM MECHANICS Time: Fri BCD 9:00-12:00 Location: ED 201 Instructor: Oleksandr Voskoboynikov 霍斯科 Phone: ext Office: 646 ED bld.4 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, Franz Schwabl, Quantum Mechanics (Fourth Edition), Springer, Yehuda B. Band and Yshai Avishai, Quantum Mechanics with applications to nanotechnology and information science, Elsevier, Class Notes. Credits: 3 (hours for weekly study 3) Grade: Home Works and Quiz 15% Midterm: 40% Final: 45% 1

2 Complex Variables Web: 2

3 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, multiparticle systems, and quantum theory of scattering are considered. In addition an introductory consideration is being given to the quantum information processing. 3

4 Introduction Wave functions, operators, observables, and quantum measurement Basic concepts of quantum mechanics 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 4

5 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. Nondegenerate 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 5

6 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 6

7 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 p. 486, 1981) (International Journal of Theoretical Physics, Vol.21, 7

8 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 8

9 #2. How does the light work? 9

10 #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 10

11 #4. How does a transistor work? ( To the electron -- may it never be of any use to anybody." JJ. Thomson's favorite toast) The First Transistor (1947) The workbench of John Bardeen and Walter Brattain at Bell Laboratories What is a crystal? What is a semiconductor? What is a quasi-electron? Why has it an effective mass 11

12 #5. What is a quantum computer? Two-state bit can not compete a multi-state quantum bit n Quantum bit Classical bit

13 #6. How is designed the Universe? The distribution of galaxies may help to confirm theories of quantum cosmology (NASA Picture ) 13

14 History 1900 M. Plank A. Einstien The electromagnetic radiation processed both a wave and a corpuscular character. It s energy is absorbed and emitted in separate portions quantaphotons E h / 2 The photons momentum is determined by the vector Plank s constant = 6.62x10-34 Js Where p k k c 14

15 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 15

16 1924 L.de Broglie A hypothesis of the wave properties of all particles of small mass 1926 E. Schrödinger The Schrödinger's wave equation v p p k m, ),, ( ), ( ) ( ), ( t t i t V t m r r r r 16

17 1927 C. J. Davison and G.P. Thomson The experimental discovery of the diffraction of electrons by crystals 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 17

18 From: Y. B. Band and Y. Avishai, Quantum Mechanics with applications to nanotechnology and information science. 18

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