# 2022/23 Undergraduate Module Catalogue

## MATH3385 Quantum Mechanics

### 15 creditsClass Size: 50

Module manager: Vincent Caudrelier
Email: v.caudrelier@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2022/23

### Pre-requisite qualifications

MATH2375, or equivalent.

### This module is mutually exclusive with

 MATH5386M Advanced Quantum Mechanics

This module is not approved as a discovery module

### Module summary

In the early years of the 20th century, it became clear that certain experimental results of atomic physics could not be adequately explained within the framework of the classical mechanics of Newton. This led to the development of quantum mechanics, which attained in the mid-1920s a coherent mathematical form which provided a basis for a proper understanding of atomic physics. This introductory module explains how quantum mechanics represents the states and observables of a system and enables statistical predictions to be made about the probable outcomes of experiments.

### Objectives

On completion of this module, students should be able to:
a) understand the basic principles of quantum mechanics and be able to apply them in simple physical situations;
b) prove and use basic results about inner products and Hilbert space and linear operators on them;
c) calculate the quantum mechanical wave function and probability distribution in a given state;
d) calculate quantum mechanical expectation values of observables;
e) solve simple eigenfunction problems for Hermitian operators;
f) predict how the state of an undisturbed quantum system evolves with time.

### Syllabus

1. Summary of the classical theory: Hamiltonian formalism, conservation laws.
2. The need for quantum mechanics, uncertainty principle, wave-particle duality, wave packets.
3. The quantum mechanics of structureless particles: the Schrödinger equation, single-particle wave function, position and momentum representation, Heisenberg uncertainty relation and the minimal wave packet.
4. Fourier integrals and the Dirac delta-function.
5. Hilbert spaces and linear operators: unitary and Hermitian operators, differential operators.
6. The mathematical formulation of quantum mechanics; eigenvalues and eigenstates.
7. The stationary Schrödinger equation and eigenstates of the Hamiltonian: simple one-dimensional potentials and their energy levels.
8. The quantum mechanical harmonic oscillator, orthogonal polynomials.

### Teaching methods

 Delivery type Number Length hours Student hours Lecture 33 1.00 33.00 Private study hours 117.00 Total Contact hours 33.00 Total hours (100hr per 10 credits) 150.00

### Opportunities for Formative Feedback

Regular example sheets.

### 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

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated