# Quantum mechanics I

## Summary

The objective of this course is to familiarize the student with the concepts, methods and consequences of quantum physics.

## Content

1. A bit of history: the crisis of classical physics. Black body radiation, photo electric effect, Compton effect.

2. Rutherford's experiment, Bohr atom, de Broglie hypothesis.

3. The Stern and Garlach experiment: quantum states and spin 1/2

4. The axioms of quantum physics: state vectors, operators, measurement, representations

5. Continuous degrees of freedom: translation operator and canonical quantization

6. Time evolution: Schrödinger's equation and Heisenberg's point of view

7. Some simple problems in one dimension

8. Central potentials, angular momentum and hydrogen atom

9. Addition of angular momentum

## Keywords

Quantum mechanics, Schrödinger equation, Heisenberg uncertainty principle, wave function, harmonic oscillator, hydrogen atom, spin, entanglement

## Learning Prerequisites

## Required courses

Basic physics and mathematics undergraduate courses

## Important concepts to start the course

Strong working knowledge of calculus and linear algebra (covered in basic math courses).

## Learning Outcomes

By the end of the course, the student must be able to:

- Compare Schrödinger's and Heisenberg's viewpoints on quantum physics
- Derive Heisenberg's uncertainty principle
- Characterize the amount of entanglement in a two-spin system
- Contextualise the postulates of quantum physics
- Explain the difference between classical and quantum physics
- Solve the quantum harmonic oscillator with the ladder operator method
- Interpret the measurement process in quantum physics
- Solve Schroendinger's equation for problems in 1,2 and 3 dimensions

## Teaching methods

Ex cathedra. Exercises prepared in class.

## Expected student activities

Students are expected to regularly attend the theory lectures and the exercise lectures. They are also expected to complete the exercises that are given on a weekly basis, as well as regularly study the learning material offered by the professor (lecture notes, exercises solutions etc).

## Assessment methods

Written exam

## Resources

## Bibliography

The key reference is :

1. "Concepts of Modern Physics" (5th edition), Arthur Beizer (McGraw-Hill Education)

2 "Modern Quantum Mechanics" (2nd edition), J.J. Sakurai, J. Napolitano (Cambridge University Press, 2017)

Other books can be occasionally consulted, most notably

3. "Mécanique Quantique I-II", Cohen-Tannoudji, Diu, Lahoë (Hermann) [Also available in English]

## Ressources en bibliothèque

- Concepts of Modern Physics / Beiser
- Modern Quantum Mechanics / Sakurai
- Mécanique Quantique / Cohen-Tannoudji

## Notes/Handbook

Lecture notes will be given at the beginning of the course

## Moodle Link

## In the programs

**Semester:**Spring**Exam form:**Written (summer session)**Subject examined:**Quantum mechanics I**Lecture:**3 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks**Type:**mandatory

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