## Module and Programme Catalogue

### 15 creditsClass Size: 115

Module manager: Dr Jiannis Pachos
Email: J.K.Pachos@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2023/24

### Pre-requisite qualifications

Level 2 Physics or equivalent

Module replaces

This module is not approved as a discovery module

### Objectives

At the end of this module students should be able to:
- Define the rules of quantum mechanics;
- Solve Schrodinger's equation when separable in Cartesian coordinates for a variety of situations including that of an electron in a magnetic field;
- Derive the results of lowest order time independent and time dependent perturbation theory and apply the results to simple physical situations;
- Describe the principles of the variational method and apply the method to simple physical problems;
- Describe and derive the methods of matrix mechanics and of Dirac formalism;
- Discuss the description of electron spin in terms of Pauli spin matrices and solve simple associated problems.

Learning outcomes
Students will be able to demonstrate knowledge, understanding and application of:

- Separation of variables method
- Spin systems and Hamiltonians with spins
- Charged particle in magnetic field
- Variational method
- Time-dependent and time-independent perturbation theories

Skills outcomes
The ability to use quantum mechanics in different scientific disciplines (chemistry, biology, etc.) and apply the same mathematics in other fields.

### Syllabus

Revision of the basic postulates of quantum mechanics. The solution of Schroedinger's equation when separated using Cartesian coordinates combining the confinement of electrons in infinite wells with period boundary conditions. Introduction of creation and annihilation operators to solve the harmonic oscillator. This leads to a description of Landau levels for charged particles in a magnetic field. Description of the Integer Quantum Hall effect. The variational method for solving difficult problems with various worked examples. Time dependent and time independent perturbation theory. Matrix mechanics leading to the description of spin states, the Pauli spin matrices and the Dirac formalism.

### Teaching methods

 Delivery type Number Length hours Student hours Lecture 22 1.00 22.00 Private study hours 128.00 Total Contact hours 22.00 Total hours (100hr per 10 credits) 150.00

### Opportunities for Formative Feedback

3 in-course, formative coursework assignments.

### Methods of assessment

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 2 hr 30 mins 100.00 Total percentage (Assessment Exams) 100.00

Students will have to complete an in-person exam at the end of the module. This will take place during the examinations period at the end of the semester and will be time bound.