# Introduction to Quantum Mechanics

Course Code : | 1001WETIKW |

Study domain: | Physics |

Academic year: | 2017-2018 |

Semester: | 1st semester |

Sequentiality: | Credit for Mathematical methods for physics I, II & III and Introduction to analytical mechanics. |

Contact hours: | 60 |

Credits: | 6 |

Study load (hours): | 168 |

Contract restrictions: | No contract restriction |

Language of instruction: | Dutch |

Exam period: | exam in the 1st semester |

Lecturer(s) | Francois Peeters |

### 1. Prerequisites *

an active knowledge of

- Dutch

- general knowledge of the use of a PC and the Internet

specific prerequisites for this course

Knowledge of elementary algebraic techniques and of differential and integral calculus.

Knowledge of classical mechanics

### 2. Learning outcomes *

- Insight in the difference between classical and quantum mechanics.
- Insight in the quantum mechanical measurement process.
- Able to solve the Schrodinger equation for simple potential problems.
- Insight in the Hilbert space formalism of quantum mechanics.
- Solving the Harmonic oscillator using differential equations and the algebraic method.
- Working with Dirac notation and switching between different representations of the same physical state.
- Solving the energy spectrum of the hydrogen atom and finding the eigenstates.
- Insight in the spin properties of electrons and combining angular momenta.
- Insight in the difference between fermions and bosons and applying it to quantum statistics.
- Insight and applying of non degenerate perturbation theory and the variational principle.

### 3. Course contents *

A. Introduction

- The birth of quantum mechanics (radiation law, photo-electric effect, ...)

- Particle-wave duality

- Interpretation of the wavefunction

- Schrodinger equation

- Position and momentum

B. Wave mechanics: one dimensional problems

- The stationary Schrodinger equation

- Potential well: bound states

- Scattering in one dimension: tunnel effect

- Resonances

C. Axiomas of quantum mechanics

- Hilbert space

- Operators and the measuring process in quantum mechanics

D. The harmonic oscillator (with inclusion of the technique of ladder operators)

E. Dirac notation

F. The hydrogen atom

- Solution for the angular part

- Solution of the radial part

- Bohr theory

- Spectrum, degeneracy, physical interpretation of the quantum numbers

G. Approximation methods

- First and second order non-degenerate perturbation theory

- Variational principle

H. Spin

- Addition of spin

- Addition of angular momenta (Clebsch-Gordon coefficients)

I. Identical particles

- Fermions and Bosons

- Exchange

### 4 International dimension*

### 5. Teaching method and planned learning activities

Personal work

### 6. Assessment method and criteria

Continuous assessment

### 7. Study material *

#### 7.1 Required reading

Course book

**7.2 Optional reading**

The following study material can be studied voluntarily :- H. Cohen-Tannoudji & B. Diu & F. Laloë, Quantum Mechanics, vol. I, Harman, Parijs, 1997;

- R.P. Feynham & R.B. Leighton & M. Sands, The Feynman Lectures on Physics, vol. III, Addison-Wesley, New York, 1965;

- D.J. Griffiths, Introduction to Quantum Mechanics, Simon & Schuster, 1995;

- S. Gasiorowicz, Quantum Mechanics, John Wiley, New York, 1996.

### 8. Contact information *

F. Peeters

Departement fysica

Campus Groenenborger, U213

Universiteit Antwerpen

email: francois.peeters@uantwerpen.be

Assistent:

B. Van Duppen

Departement fysica

Campus Groenenborger, U212

Universiteit Antwerpen

email: ben.vanduppen@uantwerpen.be