# Quantummechanics

Course Code : | 1001WETKWM |

Study domain: | Physics |

Academic year: | 2017-2018 |

Semester: | 2nd semester |

Sequentiality: | Credit for Math. methods for physics I, II & III, Introduction to anal. mechanics, General physics III, Introduction to quantum mechanics, Introduction grouptheory and Introduction field theory or enrolled for Introduction field theory |

Contact hours: | 30 |

Credits: | 3 |

Study load (hours): | 84 |

Contract restrictions: | No contract restriction |

Language of instruction: | Dutch |

Exam period: | exam in the 2nd semester |

Lecturer(s) | Jacques Tempere |

### 1. Prerequisites *

an active knowledge of

- Dutch

### 2. Learning outcomes *

- You can explain what a quantum state is and how it differs from a classical state.
- You can calculate the time evolution of a quantum state and of an expectation value, in the Schrodinger and Heisenberg pictures and with density matrices.
- You are familiar with the concept of "spin", the experiments that prove its existence, the mathematical description of this property, and you can perform the addition of spins.
- You can use density matrices to calculate quantum statistical expectation values, making use of the quantum liouville equation.
- You are familiar with Stone theorem and generators, and know how to use this to implement transformations (such as rotations) on quantum states and operators.
- You can explain the basic concepts underpinning the path-integral description of quantum mechanics.

### 3. Course contents *

We start by reviewing the differences between states in classical mechanics, in stochastic mechanics, and states in quantum mechanics. On the theoretical side, this brings us to the study of the Hilbert space, and on the experimental side we look at the Stern-Gerlach experiment, and discuss the spin of a particle in the context of quantum states and measurement.

Next, we study how states walk around in Hilbert space, and how transformations in Hilbert space take place. We describe this in term of the Stone theorem. Time evolution of quantum states is a prime example for this, and we will investigate both the Schrodinger and the Heisenberg formalisms. Another example of a transformation is a rotation. We investigate how spin states change under rotation, how combining several spins into one object is done, and how the combined object acts under rotation.

We then add statistical uncertainty back to the pure (quantum) states, leading to a description in terms of density matrices. These are shown to obey the Von Neumann equation and to allow calculation of quantum statistical expectation values.

Finally, Feynman's path integral theory is introduced as an alternative way to describe quantum mechanics, and this different angle of incidence is linked back to the Schrodinger formalism.

### 4 International dimension*

### 5. Teaching method and planned learning activities

Personal work

**5.3 Facilities for working students ***

Directed self-study (possibly with response lecture)

- Blended learning with limited amount of classroom activities in the evening

Others

For working students the evaluation criteria are adapted: 1/3 of the score comes from the blackboard tests, 1/3 from the theory exam and 1/3 from the exercise exam. Cooperation during class no longer counts. You need to inform the lecturer at the start of the course that you are a working student.

### 6. Assessment method and criteria

Continuous assessment

### 7. Study material *

#### 7.1 Required reading

Own notes taken during the course

Course notes available at the reprography

**7.2 Optional reading**

The following study material can be studied voluntarily :"Modern Quantum Mechanics", Sakurai (second edition, Pearson Education, 2011).

"Quantum Mechanics" I & II of C. Cohen-Tannoudji, B. Diu, F. Laloe, Wiley Interscience.

"Feynman Lectures on Physics, volume III", Leighton & Sands, Addison-Wesley publishing.

"Quantum Physics", Le Bellac, Cambridge University press 2007.

### 8. Contact information *

N0.17, gebouw N, Campus Drie Eiken

03 / 265 2688