Advanced Quantum Mechanics

Code:

F4034

Acronym:

F4034

Keywords
Classification	Keyword
OFICIAL	Physics

Instance: 2018/2019 - 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:A_ASTR	0	Plano de Estudos oficial desde_2013/14	1	-	6	49	162
			2
M:F	7	Official Study Plan	1	-	6	49	162

Teaching language

Portuguese

Objectives

To acquire skills, knowledge and methods to facilitate the understanding of literature results in particle physics, Physics Condensed Matter, Quantum Optics, etc.

  To know and apply the most basic techniques of direct calculation in Quantum Physics:. Changes of base, use of symmetries, perturbation theory, second quantization, theory of scattering 

To introduce  Relativistic Quantum Mechanics and Quantum Field Theory (including electromagnetic radiation).

Learning outcomes and competences

Acquisition of knowledge and skills relating to quantum concepts for reading and comprehension of research literature in areas such as,  Particle Physics, Condensed Matter, Quantum Optics etc.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Basic Quantum mechanics

Program

1. Review of basic QM
State-space, Kets, Bras, Operators and observables. Commutation relations. Complete set of compatible observables. Unitary transformations, matrix representations. Evolution operator, representations of Schroedinger and Heisenberg.
Stationary  and time-dependent perturbations.  Fermi golden rule.
 Mixtures and pure states. Density matrix.

2.Introduction to Quantum Information
Entanglement. Von Neuman entropy. Von Neumann measurements. 
Bell Inequalities
No Cloning theorem. Quantum cryptography. Dense Coding and teleportation
Quantum Computation. Circuit Model. Quantum Algorithms

2.Symmeties and unitary transformations
 Discrete and continuous symmetries. Irreducible representations; quantum numbers
 Rotation group SO(3). Angular momentum and spin. Operator Representations 

3 Identical Particles
Quantification of coupled oscillators. Normal modes and Bosons
Fock space and second quantization. Fermions. Field operators.

5 Relativistic Quantum Mechanics
Dispersion relations, field equations and quantification.
The Weyl-Dirac equation in 2 + 1 D and graphene
Dirac equation. Simple solutions.

6. Electromagnetic Filed
Quantizatiom  of a scalar field
 Quantization of the electromagnetic field.Radiation states 
Phase operators and coheren states.
Interaction matter-radiation  in dipolar approximations. Selection rules.

 

Mandatory literature

Baym Gordon; Lectures on quantum mechanics. ISBN: 0-8053-0667-6
Weinberg Steven 1933-; Lectures on quantum mechanics. ISBN: 9781107028722
Sakurai J. J. 1933-1982; Modern quantum mechanics. ISBN: 0-201-53929-2
Sakurai J. J. 1933-1982; Advanced quantum mechanics

Teaching methods and learning activities

Lectures; self-study. Autonomous problem solving aimed at developing the ability to apply quantum mechanics to fields such as condensed matter, particle physics, optics .

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	70,00
Teste	30,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	120,00
Frequência das aulas	42,00
Total:	162,00

Eligibility for exams

No requirements

Calculation formula of final grade

1. Homework assigments (3)   30%
2. Examination                          70%

Special assessment (TE, DA, ...)

N/A

Classification improvement

General FCUP rules for exam component