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2017　Exercises in Quantum Mechanics III a

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Academic unit or major
Physics
Instructor(s)
Saito Susumu  Takahashi Kazutaka  Adachi Satoshi 
Class Format
Exercise     
Media-enhanced courses
Day/Period(Room No.)
Mon7-8(W621)  Thr7-8(W621)  
Group
a
Course number
ZUB.Q314
Credits
2
Academic year
2017
Offered quarter
3Q
Syllabus updated
2017/9/20
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

The course treats fundamental and applications of quantum mechanics. By treating various systems and methods, we study nontrivial quantum effects observed in may-body systems. Treated systems are: nonlinear systems, time-dependent systems, and many-body (Bose, Fermi, and spin) systems. Treated methods are: perturbation theory, field quantization, variational method, and density operator, and so on.
This course will allow students to analyze various systems in quantum mechanics using methods treated in it.

Student learning outcomes

(1) Calculate corrections of energy levels and states of a system with the method of perturbation
(2) Understanding of the field quantization and treat particle creation and annihilation processes in many-body systems
(3) Evaluate many-body effects in various systems

Keywords

Perturbation, identical particles, field quantization, variational method, density operator, quantum entanglement

Competencies that will be developed

✔ Specialist skills Intercultural skills ✔ Communication skills Critical thinking skills ✔ Practical and/or problem-solving skills

Class flow

Problem sheet is dstributed every week. Students are expected to solve problems at home and to present answers on blackboard. Presented answers are discussed.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Overview (approximation methods, indistinguishablity of identical particles, field quantization, many-body effects) Explain the significance of approximation methods and the physical meaning of field quantization
Class 2 Perturbation theory of stationary states (1) （perturbative expansion, formula in nondegenerate case, simple examples) Calculate energy level and wavefunction corrections in a harmonic oscillator system with a perturbation
Class 3 Perturbation theory of stationary states (3) (general properties of perturbation, validity of the approximation, level dynamics) Discuss general properties of perturbation theory
Class 4 Perturbation theory of stationary states (3) (formula in degenerate case, examples in systems with many degerees of freedom) Explain how the perturbation formula is modified in degenerate case and calculate corrections in a simple example
Class 5 Time-dependent perturbation (interaction picture, perturabation formula, Fermi golden rule) Calculate correction terms in a typical time-dependent system and discuss physical meaning of the result
Class 6 Absorption and emission of light by atoms (cavity radiation, Planck formula, spontaneous emission, stimulated emission, Einstein coefficients, selection rule) Calculate Einstein coefficients by applying perturbation theory
Class 7 Time-dependent systems (time-periodic system, dynamical invariant) Find general solution of the Schroedinger equation in time-periodic systems
Class 8 Adiabatic approximation (adiabatic state, Landau-Zener transition, geometric phase) Calculate an approximate solution of the Schroedinger equation in a weakly time-dependent system
Class 9 Many-body systems (1) Identical particles (statistics of identical particles, Bose/Fermi statistics, symmetry/antisymmetry of wavefunction) Explain how the indistinguishablity of the identical particles brings Pauli exclusion principle and Bose-Einstein condensate
Class 10 Many-body systems (2) Field quantization (creation and annihilation operators, field quantization) Explain how the creation and annihilation operators are used to describe physical phenomena
Class 11 Many-body systems (3) Applications of Bose/Fermi systems (Helium atom, Bose-Einstein condensate, Hubbard model) Explain general properties of quantum many-body systems
Class 12 Many-body systems (4) Applications of spin systems (magnetic systems, Heisenberg model) Find the ground state of a simple quantum spin system and explain how it is different from that of the corresponding classical system
Class 13 Variational method (general considerations, Hatree/Hartree-Fock approximation, Mean-field theory) Explain mean-field approximation in many-body systems
Class 14 Density operator (Pure and mixed states, von Neumann equation, Bloch vector) Explain the difference between pure and mixed states
Class 15 Quantum entanglement (decomposition of composite systems, reduced density operator, Bell's inequality and its violation) Explain quantum-specific properties in many-body systems

Textbook(s)

unspecified

Reference books, course materials, etc.

J.J. Sakurai "Modern Quantum Mechanics"

Assessment criteria and methods

Homework (50%) and presentation (50%). Homework is to assess whether students can give the correct answer on the problem and the report is written properly. Presentation is checked to see a clear explanation is given and proper replies to questions are made.

Related courses

  • ZUB.Q204 ： Quantum Mechanics I
  • ZUB.Q206 ： Quantum Mechanics II
  • ZUB.S310 ： Thermodynamics and Statistical Mechanics II

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Quantum Mechanics I and II

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