Quantum mechanics I [SPHYB206]

Learning outcomes

The concept of quantum and its consequences

The fondamental equation (Schrödinger) and the postulates of quantum mechanics

The lathematical tools of basic quantum mechanics

Objectives

Content

The lecture proposes an introduction to quantum concepts. After an historical aspect, the formalim of QM is presented and the first consequences on the physical properties of matter and radiation are evidenced. An important part is devoted to the mathematical tools that allow to apprehend the formalism and the postulates. Purely quantum concepts (spin, localisation) are explicited and their consequences on the comprenhension of the world and of the technoloy explicited.

Table of contents

1 The quanta

1.1 Light and photons

1.2 Matter and quanta

2. Schrödinger equation and first consesuances

2.1 The wave function and Schrödinger equation

2.2 Wave paquets and particles

2.3 Stationnary states and state superpositions
2.4 Quantum wells and barriers at 1D

2.5 Boundary conditions

2.6 Examples of 1D systems

3 Mathematical tools
3.1 State space, scalar product and Dirac Notation
3.2 Operators and observavbles
3.3 Complete set of commuting operators
3.4 Representations . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Wave mechanics and matrix mechanics
3.6 Tensorial product of space states

4 Postulates and their consequences
4.1 State of a system
4.2 Physical quantities and observables
4.3 Result of a measurement
4.4 probability of measurement
4.5 Projection
4.6Time evolution
.
5 Statistical description of QM
5.1 Statistical indicators
5.2 Heisenberg Inegality
5.3 Evolution of the mean value of an observable .
5.4 Density matrix and operator

6 Other purely quantum concepts
6.1 The view of Schrödinger, Heisenbert and Interaction
6.2 Classical Limits and Ehrenfest theorem
6.3 The spin
6.4 Determinism, locality, Intrication and hidden variables
6.5 Information, communication et Quantum Computer