# MPhys Physics

Year of entry: 2021

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## Course unit details:Introduction to Quantum Mechanics

Unit code PHYS20101 10 Level 2 Semester 1 Department of Physics & Astronomy No

### Overview

Introduction to Quantum Mechanics

### Pre/co-requisites

Unit title Unit code Requirement type Description
Mathematics 1 PHYS10071 Pre-Requisite Compulsory
Dynamics PHYS10101 Pre-Requisite Compulsory
Vibrations & Waves PHYS10302 Pre-Requisite Compulsory
Mathematics of Waves and Fields PHYS20171 Co-Requisite Recommended

### Aims

To introduce the fundamental ideas of quantum mechanics that are needed to understand atomic physics.

### Learning outcomes

‘This course unit detail provides the framework for delivery in 21/22 and may be subject to change due to any additional Covid-19 impact.  Please see Blackboard / course unit related emails for any further updates.’

On completion successful students will be able to:

1. Understand how quantum states are described by wave functions.

2. Deal with operators and solve eigenvalue problems in quantum mechanics.

3. Solve the Schrodinger equation and describe the properties of the simple harmonic oscillator.

4. Deal with algebra of angular momentum operators and solve the simple eigenvalue problems of an angular momentum in quantum mechanics.

5. Use quantum mechanics to describe the hydrogen atom.

6. Use quantum mechanics to describe the properities of one-electron atoms.

7. Use quantum mechanics to describe the simple multi-electron systems such as helium atom and hydrogen molecule.

### Syllabus

1. Basic Elements of Quantum Mechanics

Time dependent Schrödinger equation and time evolution.

(2 lectures)

2. Commutators and compatibility

Operators and quantum states, commutation relations and compatibility of different observables.

(2 lectures)

3. The Harmonic Oscillator

Stationery states, energy levels of simple harmonic oscillator, vibrational states of a diatomic molecule

(2 lectures)

4. Orbital angular momentum

Particle in two dimensions (eigenfunctions and eigenvalues of Lz), particle in three dimensions (eigenfunctions and eigenvalues of L2 and Lz), rotational states of a diatmoic molecule.

(4 lectures)

5. Particle in a central potential

Motion according to classical physics, quantum states with certain E, L2 and Lz and the radial time-indpendent Schrodinger equation, energy levels and eigenfunctions for the Coulomb potential.

(2 lectures)

6. Hydrogen Atom

Energy levels, size and shape of energy eigenfunctions, effect of finite mass of nucleus, EM spectrum, hydrogen-like systems.

(4 lectures)

7. One-electron atoms in more details

Electron spin, Sten-Gerlach experiment, magentic moments, orbital and total angular momentum. Spin-orbit interaction, perturbation theory (1st order). Zeeman effect. Parity, radiative transitions and selection rules.

(4 lectures)

8. Multi-electron Atoms

Wave functions of identical particles. Exchange symmetry. Pauli exclusion principle. Energy states of He atom. Hartree theory. X-ray spectra. Hand's rules.

(2 lectures)

Method Weight
Other 10%
Written exam 90%

### Feedback methods

Feedback will be offered by tutors on students’ written solutions to weekly example sheets, and model answers will be issued.

### Recommended reading

Phillips, A.C. Introduction to Quantum Mechanics (Wiley)
French, A.P. & Taylor, E.F. An Introduction to Quantum Physics (Thomas Nelson)

For general background reading:
ed. Manners, J. Quantum Physics: an Introduction (IOP in association with the Open University)

### Study hours

Scheduled activity hours
Assessment written exam 1.5
Lectures 22
Tutorials 4
Independent study hours
Independent study 72.5

### Teaching staff

Staff member Role
Michael Seymour Unit coordinator

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