Quantum Mechanics I

Recommended Prerequisites

Linear Algebra, Analysis,  General Physics.

Teaching Methods

Lectures, using audiovisual media and balckboard, during which the main concepts, principles and fundamental theories of Quantum Mechanics are presented and discussed. Application to simple exemples.
Problem classes during which the student is supposed to solve by him/herself , with help whenever necessary, problems  that apply the main concepts of quantum mechanics. Evaluation  consists of a final examination, or a collection of several problem  along the semester, which will be corrected, and a final test.

Learning Outcomes

- Recognize and use basic concepts and principles of Quantum Mechanics, and apply them to simple examples.
- Know how to use the methodologies and techniques appropriate to quantum mechanics.
- Analyze, synthesize and process information. Develop critical thinking and autonomous learning. Prepare, process, interpret and communicate physics information, using relevant literature sources and appropriate tools.

Work Placement(s)

No

Syllabus

1. Introduction: limitations of Classical Mechanics and the origin of Quantum Mechanics.
2. Wave function: the Schrödinger equation, statistical interpretation of the wave function, expectation value of a physical quantity, momentum, the uncertainty principle.
3. Time independent Schrödinger equation and one-dimensional problems: infinite well, harmonic oscillator, free particle, finite square well, tunneling problems.
4. Mathematical formalism of Quantum Mechanics: Hilbert space, observables, Dirac notation, generalized statistical interpretation, generalization of the uncertainty principle.
5. Angular momentum: orbital angular momentum, angular momentum quantization, spin, angular momentum addition.
6. 3D potentials: free gas, Schrödinger equation in spherical coordinates, the hydrogen atom.
7. Perturbation theory: time independent perturbation theory for non-degenerate states and  degenerate states. Time dependent perturbation theory, Fermi Golden rule.

Head Lecturer(s)

Fernando Manuel Silva Nogueira

Assessment Methods

Final evaluation
Exam: 100.0%

Continuous evaluation
Resolution Problems: 20.0%
Frequency: 80.0%

Bibliography

Griffiths, D., Introduction to Quantum Mechanics, Prentice Hall Inc., London, 1994.
Marco Cardoso et al, Mecânica Quântica, vol 1, ISTPress, 2013
Cohen-Tannoudgi, C., Diu, B. e Laloë, F., Mécanique Quantique, Herman, Paris, 1973.