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.
(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
identical particles, second quantization, creation operator, annihilation operator, variational method, perturbation
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
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 | |
---|---|---|
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. |
Not specified
"Quantum Theory of Many-Particle Systems" (A. L. Fetter and J. D. Walecka)
"Quantum Mechanics" (L. D. Landau and E. M. Lifshitz)
Examination
Quantum Mechanics I and II