o Fundamental postulates;. Textbook: J.J. Sakurai, Modern Quantum Mechanics (
revised edition),. Lecture 02: Time-independent perturbation: non-degenerate ...
Quantum Mechanics B
2013.04 Lecture 01: QM-B: Introduction
L. Bolotov
Objectives: Approximation methods are the basis for solving application problems in real world. We review fundamental postulates and the basic concepts of quantum mechanics, and Dirac notation Outline: o o
Dirac notations; Fundamental postulates;
Textbook: J.J. Sakurai, Modern Quantum Mechanics (revised edition), Lecture 02: Time-independent perturbation: non-degenerate case Objectives: understand the basic physics of the approximate solutions for problems in quantum mechanics, time-independent perturbation, cases of non-degenerate. Outline: o o o
Time-independent perturbation, non-degenerate case; Perturbation expansion; Harmonic oscillator , quadratic Stark effect
Textbook: J.J. Sakurai, Modern Quantum Mechanics (revised edition), Chapter 5, section 5.1, 5.2, 5.3. Lecture 03: Time-independent perturbation: degenerate case Objectives: understand the basic physics of the approximate solutions for problems in quantum mechanics, time-independent perturbation, cases of degenerate states. Outline: o o o o o
The degenerate case, Secular equation; Linear Stark effect, Spin-orbit coupling, fine structure constant, Zeeman effect, van der Waals attraction of H2;
Textbook: J.J. Sakurai, Modern Quantum Mechanics (revised edition), Chapter 5, section 5.1, 5.2, 5.3. Lecture 04: Time-dependent perturbation Objectives: understand the basic physics of the solutions for time-dependent potentials with time-dependent approximation, approximate solutions to bound-state problems, interactions with radiation fields. Outline: o o o
Systems with a time-dependent potentials; Time-dependent Hamiltonian; Nuclear magnetic resonance;
Textbook: J.J. Sakurai, Modern Quantum Mechanics (revised edition), Chapter 5, section 5.5, 5.6.
Quantum Mechanics B
2013.04 Lecture 05: Time-dependent perturbation (2)
L. Bolotov
Objectives: understand the basic physics of the solutions for time-dependent potentials with time-dependent approximation, approximate solutions to bound-state problems. Outline: o o
Spin magnetic resonance; Time-dependent perturbations: step-like and harmonic perturbations ;
Textbook: J.J. Sakurai, Modern Quantum Mechanics (revised edition), Chapter 5, section 5.5, 5.6. Additional materials: Lecture 06: Interactions with the classical radiation field Objectives: apply the time-dependent perturbation theory to the interactions of atomic electron with the classical radiation field. Outline: o o o
Energy absorption and stimulated emission; Electric dipole approximation; Photoelectric effect;
Textbook: J.J. Sakurai, Modern Quantum Mechanics (revised edition), Chapter 5, section 5.7, 5.8. Lecture 07: Many-particles systems Objectives: study of two-particles systems with integer and half-integer spins. Outline: o o
Identical particles, permutation symmetry; Bosons and fermions; Two-electron system;
Textbook: J.J. Sakurai, Modern Quantum Mechanics (revised edition), Chapter 6, section 6.1- 6.3. Lecture 08: Multi-electron atom Objectives: study of many-particles systems with half-integer spins Outline: o o
Elements of the periodic table, the Hund’s rules Young tableaux for multi-electron systems ;
Textbook: J.J. Sakurai, Modern Quantum Mechanics (revised edition), Chapter 6, section 6.5, and current literature.
Quantum Mechanics B 2013.04 Lecture 09: Scattering theory: The Lippmann-Schwinger equation
L. Bolotov
Objectives: introduction to the theory of scattering and collision particles, time-independent process. Outline: o o o
The Lippmann-Schwinger equation for elastic scattering process; The Born approximation; Eikonal approximation ;
Textbook: J.J. Sakurai, Modern Quantum Mechanics (revised edition), Chapter 7, section 7.1, 7.2, 7.4,. Lecture 10: Scattering theory: Method of partial waves(1) Objectives: introduction to the theory of scattering and collision particles, time-independent process. Outline: o o
Method of partial waves for the angular momentum decomposition; Scattering of slow particles;
Textbook: J.J. Sakurai, Modern Quantum Mechanics (revised edition), Chapter 7, section 7.5. Lecture 11: Scattering theory: Method of partial waves(2) Objectives: introduction to the theory of scattering and collision particles, time-independent process. Outline: o o
Resonance scattering; Inelastic scattering;
Textbook: J.J. Sakurai, Modern Quantum Mechanics (revised edition), Chapter 7, sections 7.8, 7.11, 7.12. Lecture 12: Scattering theory: Method of partial waves(3) Objectives: introduction to the theory of scattering and collision particles, and Coulomb scattering. Outline: o o
Time-dependent potentials; Coulomb scattering;
Textbook: J.J. Sakurai, Modern Quantum Mechanics (revised edition), Chapter 7, section 7.11 and 7.12. Lecture 13: Introduction to quantum information and quantum computation Objectives: introduce general concept of entanglement, qubits, physical realisations of quantum computing Outline: o o
Quantum entanglement; Qubits, the Bloch sphere;
Textbook: M. Nielsen and I. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, 2011, and current literature.
Quantum Mechanics B
2013.04 Lecture 14: Physical realizations of quantum computing
L. Bolotov
Objectives: introduce general concept of entanglement, qubits, physical realisations of quantum computing Outline: o o o
Examples of qubit operation: demonstrations with NMR, 31P atom nuclear-spin memory, Quantum dot gates;
Textbook: M. Nielsen and I. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, 2011, and current literature. Lecture 15: Homework problems Objectives: reviewing the homework problems
