Introduction to Quantum Mechanics

Code:

IMQ01

Acronym:

IMQ

Keywords
Classification	Keyword
CNAEF	Engineering and related techniques

Instance: 2024/2025 - 2S (edição n.º 1)

Active?	Yes
Web Page:	http://villate.org/courses/quantum_mechanics/index.html
Responsible unit:	Department of Chemical and Biological Engineering
Course/CS Responsible:	Introduction to Quantum Mechanics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
IMQ	0	Syllabus	1	-	1,5	12	40,5
L.AERO	0	Syllabus	2	-	1,5	12	40,5
L.BIO	0	Syllabus	2	-	1,5	12	40,5
L.EA	0	Syllabus	1	-	1,5	12	40,5
L.EC	9	Syllabus	1	-	1,5	12	40,5
L.EEC	1	Syllabus	2	-	1,5	12	40,5
L.EGI	6	Syllabus	1	-	1,5	12	40,5
L.EM	0	Syllabus	2	-	1,5	12	40,5
L.EMAT	1	Syllabus	1	-	1,5	12	40,5
L.EMG	0	Plano de estudos oficial a partir de 2008/09	2	-	1,5	12	40,5
L.EQ	0	Syllabus	2	-	1,5	12	40,5

Teaching language

Portuguese and english

Objectives

To provide the minimum knowledge necessary to understand the fundamental concepts of Quantum Mechanics.

Learning outcomes and competences

After attending this course you should be able to explain the postulates of quantum mechanics, solve Schrödinger's equation in simple cases and understand basic quantum mechanics concepts such as particle-wave duality, uncertainty principle, exclusion principle and quantum entanglement.

Working method

Presencial

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

Linear algebra and Physics I (mechanics).

Program

1. Mathematical background. Vector spaces on the complex field. "bra" and "ket" notation. Probability theory.
2. Particles and waves. Linear momentum. Kinetic and potential energy. Angular momentum. Wave motion. Waves interference. Diffraction.
3. History. Theories of light. Balck-body radiation. Atomic models.
4. Quantum mechanics foundations. Energy quantization. Particle-wave duality. Probabilistic interpretation. Uncertainty principle.
5. Quantum model of the electron. De Broglie waves. Bose-Einstein condensation. Electrons dispersion.
6. Quantum model of light. Photons. Polarization. Malus law. Beam splitters.
7. Superposition and quantum entanglement. Coherent superposition of states. Entanglement and Bell's bases. Schrödinger's cat paradox. Quantum teleportation. quantum cloning.
8. Schrödinger equation. Solution of the one-dimensional Schrödinger: particle inside a box. Tunneling. Solution of the Schrödinger equation in three dimensions: hydrogen atom.

Mandatory literature

Zubairy, M. S.; Quantum Mechanics for Beginners, with applications to quantum communication and quantum computing, Oxford University Press, 2020. ISBN: 978-0-19-885423-4

Complementary Bibliography

Susskind, L. & Friedman, A.; Quantum Mechanics, The Theoretical Minimum, Penguin Books, 2014. ISBN: 978-0-141-97781-2
Feynman , Richard P.; The feynman lectures on physics
Jordan, T. F.; Quantum mechanics in simple matrix form, John Wiley & Sons, 1986. ISBN: 0-471-81751-1
van Dommelen, L.; Quantum Mechanics for Engineers, Author's edition, 2012

Teaching methods and learning activities

The subjects of the course will be delivered in 12 theoretical lectures. The student will have to submit the solution to a group of take-home problems and to attend a final exam.

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	70,00
Trabalho escrito	30,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	16,50
Frequência das aulas	12,00
Trabalho escrito	12,00
Total:	40,50

Eligibility for exams

Any student officially enrolled in the course who attends at least 75% of the lectures and submits the take-home problems is eligible to take the final exam.

Calculation formula of final grade

0.3 (problems' grade) + 0.7(exam's grade)

Examinations or Special Assignments

Internship work/project

Special assessment (TE, DA, ...)

Classification improvement

Observations