TEKNISKA HOGSKOLAN I LINKOPING
Institut for fysik, kemi och biologi
Iryna Yakymenko
tel.: 288947
e-mail:irina@ifm.liu.se

QUANTUM DYNAMICS, TFYA28, 6 points

Aim:

The main aim of the course is to give an exposition of the advanced concepts of quantum quantum mechanics such as time-dependent perturbation theory, theory of many-particle systems, scattering theory, quantization of electromagnetic field and relativistic quantum theory.

Course Organisation:

The course contains 32 seminars with the theory and solution of problems following a special plan. Course will be given by Iryna Yakymenko. Course language is English.

Course Literature

I.I. Yakimenko. Lecture Notes in Quantum Dynamics. For the supplementary reading the following books are recommended:
  1. Bransden B.H., C.J. Joachain. Quantum mechanics, Second edition, Pearson Education, 2000.
  2. E. Merzbacher. Quantum mechanics, 3rd edition, John Wiley and Sons, 1998.
  3. Landau L.D. and Lifshits E.M. Quantum mechanics (Non-relativistic Theory), Oxford, New York: Pergamon Press,1977.
  4. Dirac P.A.M. Principles of quantum mechanics. 4th ed, Oxford University Press, 1958 (reprinted in 1999).
  5. Messiah A. Quantum Mechanics, Two Volumes Bound as One. New York: Dover (2000).

Examination

Solution of the home problems and oral presentation.

Plan of lectures

The theory will be expounded following the book I.I. Yakimenko. Lecture Notes in Quantum Dynamics. The examples are from the Exercises in Quantum Dynamics (will be hand-out during seminars).

Lecture 1: INTRODUCTION TO QUANTUM MECHANICS: p.1-19. Vectors in Abstract Vector Space. Operators in Abstract Vector Space. Eigenvalues and Eigevectors of Operators. Matrix Representation of Operators.

Lecture 2: DIRAC FORMULATION OF QUANTUM MECHANICS: p.20-27. Vectors in Abstract Vector Space. Operators in Abstract Vector Space. Eigenvalues and Eigevectors of Operators. Matrix Representation of Operators.

Lecture 3: LINEAR HARMONIC OSCILLATOR: p.28-34. Eigenvalue Problem. Eigenvalue Problem for Number Operator. Unitary Operators.

Lecture 4: PAULI SPIN MATRICES AND SYSTEMS OF PARTICLES WITH SPIN ONE-HALF: p.35-39. Introduction. Wave Mechanics with Spin. Pauli Spin Operators.

Lecture 5: PRINCIPLES OF QUANTUM DYNAMICS: p.42-51. Evolution of Probability Amplitude and Time Dependent Operator. Schrodinger, Heisenberg and Dirac Representation. Propagator in Coordinate Representation. Feynman's Path integral Formulation of Quantum Dynamics.

Lecture 6: MEASUREMENT AND DENSITY MATRIX: p. 53-63. Heisenberg Uncertainty Principle. Complete Set of Commuting Operators. Measurement, Mixed State, Density Operator or Density Matrix. Entropy. Quantum Dynamics of Spin Systems.

Seminar 1. DENSITY MATRIX FOR PURE AND MIXED STATES. Solution of problems 1-6 from the Exercise Set.

Lecture 7: TIME-DEPENDENT PERTURBATION THEORY: p. 64-73. Introduction.Perturbation Method. Fermi Golden Rule. Periodic Perturbation. Asymptotic Behaviour of Transition Probabilities.

Seminar 2. PAULI MATRICES, TIME-DEPENDENT PERTURBATION THEORY. Solution of problems 7-11 from the Exercise Set.

Lecture 8. QUANTUM STATISTICS: p. 75-89. Physical Quantities in Quantum Statistics. Quantum Mechanical Ensembles. Applications to Single-Particle Systems. Systems of Non-Interacting Particles. Photon Gas and Planck's Law. Ideal Gas. Bose-Einstein Gases: Bose-Einstein Condensation. Fermi-Dirac Gases.

Lecture 9. THEORY OF MANY-PARTICLE SYSTEMS: p. 90-103. Variational Approach. Many-Particle System: Wave function and Hamiltonian. Hartree Equations. Hartree-Fock Equations. Jellium and the Hartree-Fock Approximation.

Lecture 10. THOMAS-FERMI APPROXIMATION AND DENSITY-FUNCTIONAL THEORY: p. 104-112. Thomas-Fermi Approximation. Principles of Density-Functional theory. Kohn-Sham Equations. Spin-Dependent Density-Functional Theory.

Lecture 11. TRANSPORT IN TWO-DIMENSIONAL SEMICONDUCTOR HETEROSTRUCTURES: p. 113-127. Introduction. Semiconductor Heterostructure and Artificial Atoms. Modulation-Doped Heterostructure. Electronic Properties of Modulation-Doped Heterostructure. Counting States. Landauer Formula: Physical Foundation. Landauer Formula: Devivation. Quantization of Conductance in Nanostructures. 0.7 Conductance Anomaly.

Lecture 12. ADDITION OF ANGULAR MOMENTA: p. 128-137. Total Spin for Two Electrons. Algebraic Approach. Total Angular Momentum, Clebsh-Gordon coefficients. Spectral Line Splitting.

Seminar 3. SPIN IN MAGNETIC FIELDS, ANGULAR MOMENTA. Solution of problems 12-14 from the Exercise Set.

Lecture 13. SECOND QUANTIZATION OF FERMION AND BOSON SYSTEMS: p. 138-148. Introduction. Creation and Annihilation Operators. Algebra of Creation and Annihilation Operators. Quantum Dynamics of Identical Particles. Quantum Field Operators and Second Quantization Formalism.

Lecture 14. TIGHT-BINDING MODEL: p. 149-151. Motion in Periodic Potentials. Tight-binding Model

Seminar 4. THEORY OF MANY-PARTICLE SYSTEMS, SECOND QUANTIZATION FORMALISM. Solution of problems 15-17 from the Exercise Set.

Lecture 15. SCATTERING: p.152-162. Introduction. Cross Section. Green's Function Approach. Born Approximation.

Lecture 16. SCATTERING: PARTIAL WAVES, PHASE SHIFTS AND RESONANCES: p. 163-171. Introduction. Partial Wave Analysis. Phase Shifts and Resonances.

Seminar 5. SCATTERING. Solution of problems 18-19 from the Exercise Set.

Lecture 17. QUANTIZATION OF ELECTROMAGNETIC FIELD: p. 172-182. Basic Idea. Quantization of Electromagnetic Field. Photon States.

Lecture 18. INTERACTION OF LIGHT WITH MATTER: p. 183-194. Emission and Absorption of Photons by Atoms. Spontaneous Emission. Planck's Formula in Quantum Theory of Radiation. Reyleigh, Thomson and Raman Scattering. Resonance Fluorescence.

Seminar 6. RELATIVISTIC ELECTRON. Solution of problems 20-23 from the Exercise Set.

Lecture 20. EINSTEIN-ROSEN-PODOLSKI PARADOX AND BELL'S INEQUALITIES: p. 204-207.