Teaching	E-mail

Chung-Yu Mou

Course description (課程目標)

本課程乃針對大四與大四以上的同學設計， 藉由詳細有系統的解說使同學掌握量子力學的基本原理。
為了讓同學一窺與這些原理有關的新發展， 將盡可能涵蓋新的題目如 Berry phase、AC effect。
對於其他有趣的題目如 quantum computer 或 由量子力學所引發概念上的問題， 可指導同學於課後討論。
This course is particularly designed for senior undergraduate students and 1st year graduate students.
Its purpose is to develop students' understanding of basics of quantum mechanics, and through systematic
illustrations, it tries to develop students' grasping the fundamental principles of quantum mecahnics.
In addition to standard topics covered in quantum mechanics, students will also explore subjects that are
relatively new, such as Berry phase, AC effect, and quauntum computer with emphasis on
the usage of the basic principles.

(I) midterm: 11/9 (Friday morning), final: 1/5 (Friday evening)

• Foundations and Dirac notations
• Simple 1D systems
• Classical limit and the WKB approximation
• Uncertainty principle
• Particles in E.M. fields
• AB & AC effects
• Introduction to Feynman's path integral formulation
• Quantum harmonic oscillators
• Dirac's method
• Coherent states
• Identical particles
• Introduction to method of second quantization
• Symmetries and their consequences

(II) midterm: April 12 (Friday), final: June 14 (Friday)

• Theory of angular momentum & rotations
• Elementary theory of orbital and spin angular momentum
• Particle in central potentials
• Time-reversal symmetry in spin-1/2 systems
• Addition of angular momenta
• Usage of Wigner-Eckart theorem
• Bell's inequality
• Approximate methods
• Variational method
• Non-degenerate & degenerate time-independent perturbation theories
• Time-dependent perturbation theory
• Adiabatic theorem & the Berry phase
• Introduction to scattering theory
• Born approximation & method of partial waves
• Introduction to relativistic quantum mechanics
• The Klein-Gordon & Dirac equations (single-particle theories)

Textbooks

• Principles of Quantum Mechanics, 2nd edition, by R. Shankar
• Modern Quantum Mechanics, 2nd edition, by J.J. Sakurai

References

• Feynman's Lectures on Physics, Vol.3
• Quantum Mechanics, I & II, by A. Messiah
• Quantum Mechanics, 3rd edition, by Landau & Lifshitz
• Quantum Mechanics: Fundamental, 2nd edition, by Gottfried and Yan
• Quantum Mechanics (Julian Schwinger), edited by Berthold-Georg Englert
• Quantum Computation and Quantum Information, by Nielsen and Chuang
• The ghost in the atom (原子中的幽靈), by P.C.W. Davies and J.R.Brown, 譯者： 史領空, 出版社：貓頭鷹 (2005)

Course grading (計分方式)

• Grades for your performance in this course will be awarded in accordance with the scheme:
  total grade = homework 1/3 + midterm exam 1/3 + final exam 1/3
• Extra grades will be given to those who successfully solve problems marked as "bonus problem".
• The assessment of homework is not soly based on total sum of grades from each homework.
  The final grade for homework is determined by the number of successfully-answered problems in
  midterm and final that are identical to problems in homeworks.
  (作業成績之決定取決於小考或期中考中與作業一致的題目是否答對)