# Theoretical Physics 3 (Quantum Mechanics)

## Module PH0007 [ThPh 3]

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

### Module version of SS 2019

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions | ||||
---|---|---|---|---|

SS 2020 | SS 2019 | SS 2017 | SS 2016 | SS 2011 |

### Basic Information

PH0007 is a semester module in German language at Bachelor’s level which is offered in summer semester.

This Module is included in the following catalogues within the study programs in physics.

- Mandatory Modules in Bachelor Programme Physics (4th Semester)
- Physics Modules for Students of Education

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workload | Contact hours | Credits (ECTS) |
---|---|---|

270 h | 120 h | 9 CP |

Responsible coordinator of the module PH0007 in the version of SS 2019 was Norbert Kaiser.

### Content, Learning Outcome and Preconditions

#### Content

Introduction

Literature

1 Particle and Waves

2 States and measurements

3 Time Evolution

4 One-dimensional potentials

5 Approximative Methods

6 Symmetry transformatikons

7 Schrödinger equation in the central field

8 Applications: Two-state systems

9 Mixed states: density matrix

10 Entangled states, entanglement entropy

A Mathematical foundations

#### Learning Outcome

After successful participation, students are able to:

1. understand the implications of Schrödinger's equation and how to describe states with wave functions

2. solve Schrödinger's equation for one-dimensional problems and interpret the solution

3. apply the bra-ket formalism

4. solve the hydrogen atom and other basic problem in three-dimensions

5. explain the concept of spin and the Stern Gerlach experiment

6. solve problems that involve two quantum states

7. solve problems using approximate methods

8. understand the concept of density matrices and quantum entanglement

#### Preconditions

PH0005, PH0006, MA9201, MA9202, MA9203, MA9204

for students studying bachelor of science education mathematics / physics: PH0005, PH0006, PH0003, MA9937, MA9938, MA9939, MA9940

### Courses, Learning and Teaching Methods and Literature

#### Courses and Schedule

Type | SWS | Title | Lecturer(s) | Dates |
---|---|---|---|---|

VO | 4 | Theoretical Physics 3 (Quantum Mechanics) | Garbrecht, B. |
Wed, 10:00–12:00, PH HS1 Mon, 08:30–10:00, PH HS1 |

UE | 2 | Open Tutorial for Theoretical Physics 3 (Quantum Mechanics) |
Responsible/Coordination: Garbrecht, B. |
Wed, 12:00–14:00, ZEI 0001 |

UE | 2 | Exercise to Theoretical Physics 3 (Quantum Mechanics) |
Responsible/Coordination: Garbrecht, B. |
dates in groups |

UE | 2 | Large Tutorial to Theoretical Physics 3 (Quantum Mechanics) | Kaiser, N. |
Wed, 16:00–18:00, PH HS1 |

#### Learning and Teaching Methods

Lecture: black-board presentation

Open tutorial: The open tutorial provides the opportunity for solving the exercises for oneself or as a group. The open tutorial is overseen by different tutors an leaves room for further discussions and exchange with other students.

Tutorial: The tutorial is held in small groups. In the tutorial the weekly exercises are presented by the students and the tutor. They also provide room for discussions and additional explanations to the lectures.

#### Media

Blackboard or powerpoint presentation

accompanying informations on-line

#### Literature

D.J. GRIFFITHS, Introduction to Quantum Mechanics, Prentice Hall.

Good introductory materials.

F. SCHWABL, Quantenmechanik, Springer.

Highler level of detail and good presentation

J.L. BASDEVANT, J. DALIBARD, Quantum Mechanics, 2005.

Cleanly worked out; discusses both the mathematical basics as well as conceptual questions. Focuses allso an new experiments and applications.

R. SHANKAR, Principles of Quantum Mechanics, 2011.

Includes a mathematical description. Quite detailed.

M. LE BELLAC, Quantum Physics, 2012. Sorgfältige Darstellung, aber auf

quite high-level. Not useful as the only sorce for the first contact with Quantum Mechanics

J.J. SAKURAI, J.J. NAPOLITANO Modern Quantum Mechanics, 2010.

Good textbook which is also on a higher level.

R.P. FEYNMAN, R.B. LEIGHTON, M. SANDS, Feynman Vorlesungen über Physik III: Quantenmechanik, 1988.

Feynmans remarkable style with very detailed explanations. Not as systematic as other books.

### Module Exam

#### Description of exams and course work

There will be a written exam of 90 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using calculation problems and comprehension questions.

For example an assignment in the exam might be:

- set-up and solution of the Schrödinger equation for a particle in a potential and interpretation of the solutions
- interpretation of the physical consequences of a given wave function

Participation in the exercise classes is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.

There will be a bonus (one intermediate stepping of "0,3" to the better grade) on passed module exams (4,3 is not upgraded to 4,0). The bonus is applicable to the exam period directly following the lecture period (not to the exam repetition) and subject to the condition that the student passes the mid-term of obtaining 80% of the total points of the problem sets.

#### Exam Repetition

The exam may be repeated at the end of the semester.