Unit information: Mechanics, Oscillations and Quantum Mechanics I in 2021/22

Unit name	Mechanics, Oscillations and Quantum Mechanics I
Unit code	PHYS20028
Credit points	20
Level of study	I/5
Teaching block(s)	Teaching Block 1 (weeks 1 - 12)
Unit director	Dr. Skrzypczyk
Open unit status	Not open
Pre-requisites	PHYS10005, PHYS10006, or equivalent.
Co-requisites	None.
School/department	School of Physics
Faculty	Faculty of Science

Description including Unit Aims

Classical Physics comprises much of the core of physics, built on the foundations developed in the 17th to 19th centuries and underpinning all of "modern" physics. This course also provides the first formal introduction to Quantum Physics, one of our most basic theories of physics, which underpins everything ranging from atoms and molecules, to solid state physics, to quantum field theory and nuclear and particle physics.

This unit builds on level C/4 material in the areas of Oscillations and Mechanics. Methods to analyse the motion of systems with many degrees of freedom are presented. The significance of conservation principles in mechanics is discussed, using central force motion as an example system. Mechanics in non-inertial reference frames is introduced. The treatment of rotation and angular momentum is extended into three dimensions, allowing a full understanding of the motion of rigid bodies.

The course covers the basic concepts of non-relativistic quantum mechanics, based upon the Schrödinger wave equation, and focuses solely on the behaviour of a single particle in one, two or three dimensions.

Aims:

To introduce students to a core of classical physics including rigid body mechanics, central force motion, and coupled oscillators. To cover the basic conceptual and mathematical framework of quantum mechanics and to apply it to study the mechanics of a single particle

Intended Learning Outcomes

Students will:

• appreciate the behaviour of systems of coupled oscillators
• be able to describe qualitatively and quantitatively motion under central forces
• understand the modifications to laws of motion experienced in a non-internal reference frame
• gain a qualitative understanding of the general motion of rigid bodies, and be able to carry out full analysis of simple systems
• Be able to describe the photoelectric effect, the Bohr atom and the de Broglie wavelength.
• Be able to write down the Schrödinger wave equation and solve for the wave function in a number of simple situations
• Understand the statistical interpretation of the wave function, as well as be able to normalise it and use it to calculate probabilities and expectation values.
• Know what the position and momentum operators are, and to be able to apply the Heisenberg Uncertainty principle.
• Be able to derive the time-independent Schrödinger equation and define stationary states.
• Be able to write down the Hamiltonian operator, and understand what it means to find its energy eigenvalues and eigenstates.
• Understand the necessary boundary conditions on wave functions, including continuity.
• Be able to solve the Schrödinger equation for the infinite square well potential and for the Harmonic Oscillator.
• Understand what it means for energy eigenstates to be orthogonal and to form a complete set.
• Be able to apply the superposition principle.
• Be able to describe the motion of a free particle, including how to form wave packets, and the notions of group and phase velocity.
• Know what momentum eigenstates are, as well as the momentum wave function
• Be able to write down the probability current and the continuity equation.
• Understand quantum mechanical tunnelling.
• Be able to calculate the reflection and transmission coefficients of a particle impinging upon a potential step.
• Be able to write down the Schrödinger equation in three dimensions in Cartesian and in spherical polar coordinates.
• Be able to separate variables to obtain the radial and angular equations, and to appreciate the role of spherical harmonics as solutions to the latter when there is spherical symmetry.
• Be able to solve the Schrödinger equation for the three-dimension infinite box and to understand what it means to have degenerate energy eigenstates.

Teaching Information

The unit will be taught through a combination of

• asynchronous online materials, including narrated presentations and worked examples
• synchronous group problems classes, workshops, tutorials and/or office hours
• asynchronous directed individual formative exercises and other exercises
• guided, structured reading

Assessment Information

Written timed, open-note examination (80%) Coursework (20%).

Resources

If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. PHYS20028).

How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours of study to complete. Your total learning time is made up of contact time, directed learning tasks, independent learning and assessment activity.

See the Faculty workload statement relating to this unit for more information.

Assessment
The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit. The Board considers each student's outcomes across all the units which contribute to each year's programme of study. If you have self-certificated your absence from an assessment, you will normally be required to complete it the next time it runs (this is usually in the next assessment period).
The Board of Examiners will take into account any extenuating circumstances and operates within the Regulations and Code of Practice for Taught Programmes.