Advanced Quantum Mechanics

Code:

F401

Acronym:

F401

Keywords
Classification	Keyword
OFICIAL	Physics

Instance: 2012/2013 - 1S

Active?	Yes
Responsible unit:	Department of Physics and Astronomy
Course/CS Responsible:	Master in Physics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
M:F	12	Plano de Estudos do Mestrado em Física	1	-	7,5	-
M:M	0	PE do Mestrado em Matemática	1	-	7,5	-
			2

Teaching language

Portuguese

Objectives

Learn the differences between the basic and advanced quantum mechanics.  Obtain the mathematical techniques proper to the many-body and relativistic systems. Develop practical knowledge to calculate the observable characteristics of these systems. The knowledge of the basic quantum mechanics and mathematical analysis are necessary.

Learning outcomes and competences

Knowledge of theoretical bases and practical methods to calculate the characteristics of many-body systems, involving the relativistic effects.

Working method

Presencial

Program

1. Many-body systems. Identity of quantum particles. Operators of permutations. Symmetric group Sn. Operators of observables. Quantum states of N identical (independent) particles. Bosons and fermions. Pauli exclusion principle. States of 1,2 and N fermions. Second quantification. Field operators. 2. Symmetries and conservable values . Group of space translations. Group of space rotations. Eigen-functions of angular momenum. Euler angles. Spin rotations. Relation between orbital e spin angular momenta. Total angular moment. Addition of angular moments. Addition ofe 2 moments. Recursive relations for Clebsch-Gordan coefficients. Vectorial operators and selection rules. Tensorial operators. Wigner-Eckart theorem. Ortogonality of Wigner functions. Isotopical spin. Inversion symmetries. 3. Quantum theory of scattering. Laboratory and center of mass reference systems. Main characteristics of scattering. Relation between scattering potencial and scattering amplitude. Born approximation. Optical theorem. Analytic properties of scattering amplitude and phases. Case of attractive potential: resonances with bound state. Low energy resonances. Scattering of identical particles. Identity and isotopical spin. 4. Electromagnetic radiation and its interaction with matter. Maxwell equations and electromagnetic waves. Interaction of light with matter. Light absorption (non-quantized field approximation). (Second) quantization of electromagnetic field. Thermodynamical equilibrium between light and matter, Einstein relations. Multipolar moments of radiation: electric dipolar moment, magnetic dipolar moment, electric quadrupolar moment.  Multipolar absorption and selction rules. Natural linewidth. Light scattering in quantum treatment. Raman scattering. Quantum states of radiation: |n>, |phi> and coherent states. 5.Relativistic quantum mechanics. Klein-Gordon equation. Particles e antiparticles. 1st order K.-G. equation. Dirac equation. Lorentz transformations of 4-spinors. Non-relativistic limit of Dirac equation, Pauli equation. 6. Green function methods. Green functions for classical problems. F.G. in quantum mechanics: stationary and time-dependent Schroedinger equations, Klein-Gordon equation. F.G. within 2nd quantization formalism. Relation between f.G. and physical characteristics of a system. Interaction representation for f.G.

Recommended literature

1. G. Baym. Lectures on Quantum Mechanics. Benjamin, 1969. 2. W. Greiner. Quantum Mechanics. Special Chapters. Springer, 1989. 3. L. Landau & E. Lifshitz. Quantum Mechanics (Non-relativistic Theory). Pergamon, 1977. 4. H.J. Lipkin. Quantum Mechanics. New Approaches to Selected Topics. North Holland, 1973. 5. J. Sakurai. Advanced Quantum Mechanics. Addison-Wesley, 1967. 6. S. Flügge. Practical Quantum Mechanics, Vol. I, Springer, 1971.

Additional literature

S. Gasiorowicz. Quantum Physics. Wiley & Sons, 1974.

K. Gottfried. Quantum Mechanics. Vol. I: Fundamental Problems. Addison-Wesley, 1989.

Mandatory literature

Baym Gordon; Lectures on quantum mechanics. ISBN: 0-8053-0667-6
Landau L. D. (Lev Davidovic) 1908-1968; Quantum mechanics. ISBN: 0-08-020940-8
Lipkin Harry J.; Quantum mechanics. ISBN: 0-7204-0258-1
Sakurai J. J. 1933-1982; Advanced quantum mechanics
Gasiorowicz Stephen; Quantum physics. ISBN: 0-471-29280-X
Flugge S; Practical Quantum Mechanics

Teaching methods and learning activities

Lecturing of the course with use of multimedia. curso com uso dos métodos multimédia. Seminários Theorical-practical seminars including mini-talks to present the home works.

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Final test and final exam	Exame	3,50	75,00	2013-01-09
Mini talks on home work	Prova oral	22,00	25,00
	Total:	-	100,00

Amount of time allocated to each course unit

Description	Type	Time (hours)	End date
Lecturing of the course	Frequência das aulas	42	2013-01-09
	Total:	42,00

Eligibility for exams

The mínimum attention rate is 75% of lectures to be admitted for the final exam. 

Calculation formula of final grade

The written exam note (may result from the note for the test work) accounts for 75% of the final note, the resting 25% result from evaluation of theorical-practical home works during the semester.