Course Overview

Quantum mechanics lies at the core of the understanding of electronic
properties and the concepts of matter cohesion, organization and
transformation together with all the response properties associated to
the physics of measurement. The objective of this course is to provide
students with the principles and formalism of quantum mechanics
together with various illustrative applications casted in a consistent
framework.This course provides students coming from a Chemistry,
Physics and Physical Chemistry Bachelor with a better understanding of
the molecular basis of the physical and chemical properties of matter.

Beyond the few exactly solvable case studies, this course intends to
focus specifically on approximate quantum mechanics tackling the N
body problem of interacting particles so as to make students aware of
the notions of modelling. This includes variation and perturbation
schemes, based on the analysis of the physical relevance of quantum
fluctuations with respect to the level of understanding and accuracy
required in a given problem.

Matter- Light interaction is eventually introduced in the dipolar
approximation, using time dependent perturbation theory, introducing
the photo-physical elementary processes of resonant absorption,
resonant stimulated emission and spontaneous emission. This is
illustrated on the vibronic molecular spectroscopy in the
IR,UV/visible regimes.  

At the end of the course, students are able to formalise a problem in
terms of quantum models that can be tackled either variationaly or
using perturbation theory.

Learning Achievement

Competence

Course prerequisites

> Students must have:

- Basic knowledge of “Quantum mechanics” (undergraduate level).

Grading Philosophy

Type of assessment / first session: homework assignment (20% weight
ofoverall mark), Mid-term written exam (20% weight of overall
mark),final written exam (60% weight of overall mark).
_
_

_In case of failures/second session: written exam (60% weight of
overallmark), recall of the first session intermediate evaluation
(40%weight of overall mark)._

Course schedule

> Lectures:

- Mathematical tools: Vector spaces, Hermitian product, Matrices and
linear algebra.
- Quantum states, Superposition principle, Hilbert spaces.
- Observables: Operators, Matrix representation, Measurement and
eigenvalue equations, Mean values.
- The Schrödinger equations Time dependent and time independent.
- Restricted Hilbert spaces: Variation theory and the linear
variation method.
- Rayleigh-Schrödinger perturbation theory.
- Variation-Perturbation and effective hamiltonians.
- Time dependent perturbation theory.
- Interaction with an electromagnetic field - Multipolar
decomposition.
- Transition moments, polarisability and selection rules.
- Einstein theory in the optical domain.

Course type

> 154 hours of lectures and tutorials: - 51 contact hours (28h lectures, 23h tutorials). - 100 hours self-study. - 4.5 hours written assessment exam.

Online Course Requirement

Instructor

Other information

Duration: 12 weeks (Fall Semester)

Language of instruction: English
Mode of delivery: Face-to-face teaching: lectures, tutorials.

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