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2017　Quantum Mechanics III

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Academic unit or major
Physics
Instructor(s)
Saito Susumu 
Class Format
Lecture     
Media-enhanced courses
Day/Period(Room No.)
Mon5-6(H112)  Thr5-6(H112)  
Group
-
Course number
ZUB.Q313
Credits
2
Academic year
2017
Offered quarter
3Q
Syllabus updated
2017/3/21
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

This course covers fundamentals and applications of quantum mechanics.We first study the basic methods and the concept for quantum many-body systems, the second quantization and field operators both for bosons and fermions. Next, we study the variational methods used for complex systems. Finally, we study the perturbation theory for stationary systems and for he time-dependent systems.

Student learning outcomes

(1) Understand field quantization and work with particle creation and annihilation processes in many-body systems
(2) Understand the difference and the characteristics of several trial functions in the variational methods for Fermions.
(3) Calculate corrections of energy levels and states of a system with the method of perturbation

Keywords

identical particles, second quantization, creation operator, annihilation operator, variational method, perturbation

Competencies that will be developed

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

Class flow

Mostly the blackboard is used to explain the details of the mathematical derivations. At the same time the emphasis is put on the insight into the physical aspects of the system in order to achieve the deep understanding of the quantum mechanics.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Overview of this lecture Hamiltonian for many-particle systems Understand the overview of the lecture, and learn the Hamiltonian operator of the many-particle systems
Class 2 Fermions and Bosons Understand the statistical characteristics of the wavefunctions for fermions and bosons
Class 3 symmetrized products for bosons Understand the symmetrized products and the matrix elements of the one-particle and two-particle operators between the symmetrized products
Class 4 creation and annihilation operators and the Hamiltonian Introduce the Hilbert space where the occupation numbers play the independent variables, and also the creation and annihilation operators defined in the spade. Also understand the Hamiltonian written with those operators.
Class 5 field operators and second quantization Introduce field operators and understand that they give a beautiful and concise Hamiltonian expression.
Class 6 anti-symmetrized products for fermions Understand the anti-symmetrized products and the matrix elements of the one-particle and two-particle operators between the anti-symmetrized products
Class 7 field operators and second quantization for fermions Understand the field operators for fermions, their differences from those for bosons, and the second quantization for fermions
Class 8 variational principle in quantum mechanics, and variational methods and trial functions. Understand the variational principle, and the variational method and trial functions
Class 9 Hartree approximation and Hartree-Fock approximation Understand the basic but important approximations, Haree and Hartree-Fock approximations
Class 10 Perturbation theory and first-order perturbation Understand the concept of the perturbation theory in quantum mechanics, and the first-order perturbation theory
Class 11 Second order perturbation theory Understand the second-order perturbation theory
Class 12 applications of the perturbation theory Understand the perturbation theory applied to the harmonic oscillator
Class 13 perturbation theory for degenerated systems Understand how to apply the perturbation theory to the systems with the degenerary
Class 14 time-dependent perturbation theory Understand the perturbation theory with time-dependent perturbation potential
Class 15 Transition probabilities and Fermi's golden rule Summary Understand the transition probabilities and the Fermi's golden rule. Summary of the lecture.

Textbook(s)

Not specified

Reference books, course materials, etc.

"Quantum Theory of Many-Particle Systems" (A. L. Fetter and J. D. Walecka)
"Quantum Mechanics" (L. D. Landau and E. M. Lifshitz)

Assessment criteria and methods

Examination

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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