# Modules

### PHY2020 : Principles of Quantum Mechanics

• Offered for Year: 2018/19
• Module Leader(s): Professor Nikolaos Proukakis
• Owning School: Mathematics, Statistics and Physics
• Teaching Location: Newcastle City Campus
##### Semesters
 Semester 1 Credit Value: 10 ECTS Credits: 5.0

#### Aims

To discuss mathematically the wave theory of matter by analysing the Schrodinger equation and introduce basic operator algebra and quantum-mechanical postulates.

Module Summary

Quantum mechanics is the theoretical framework used to describe the most fundamental properties of matter. It has a rich mathematical structure and it has provided the impetus for many advances in mathematics. It also has many practical applications, including the modelling of atoms, molecules and semiconductors. Recently, quantum theory has been used extensively to model superfluids and supercooled gases, and there are even attempts to build computers which function by the laws of quantum mechanics.

This module discusses the wave formulation of quantum mechanics in the context of the one-dimensional Schrodinger equation, which is mathematically solved in various trapped problems, including box and quadratic potentials, and open-boundary cases. The course introduces the more mathematical aspects of quantum mechanics including its formal structure based on the fundamental postulates, and the role and importance of operator algebra in describing such systems. Simple extensions to three dimensions are also touched upon, including a brief discussion of relevant quantum numbers.

#### Outline Of Syllabus

Reminder of Preliminary concepts: de Broglie and Planck relations and the uncertainty principle; brief introduction to distribution functions. Schrodinger's equation and its solutions in an infinite- and finite-height box and in a harmonic oscillator potential; the correspondence principle and superposition states. The formal rules of quantum mechanics: basic postulates, operator algebra; the harmonic oscillator revisited. Open boundary problems, reflection and transmission coefficients. Basic introduction to the 3D Schrodinger equation.

#### Teaching Methods

##### Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision lectures
Scheduled Learning And Teaching ActivitiesLecture61:006:00Problem classes
Scheduled Learning And Teaching ActivitiesLecture221:0022:00Formal lectures
Guided Independent StudyAssessment preparation and completion111:0011:00Revision for unseen Exam
Guided Independent StudyAssessment preparation and completion11:301:30Unseen Exam
Guided Independent StudyAssessment preparation and completion55:0025:00Written assignments
Scheduled Learning And Teaching ActivitiesDrop-in/surgery61:006:00Drop-ins in lecture room
Guided Independent StudyIndependent study51:005:00Assignment review
Guided Independent StudyIndependent study121:3021:30Studying, practising and gaining understanding of course material
Total100:00
##### Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the studentsâ€™ abilities at applying the theory to solving problems. Drop-ins are used to identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. Office hours provide an opportunity for more direct contact between individual students and the lecturer.

#### Assessment Methods

The format of resits will be determined by the Board of Examiners

##### Exams
Description Length Semester When Set Percentage Comment
Written Examination1201A90unseen
##### Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises1M10N/A
##### Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. Written assignments (approximately 5 pieces of work of approximately equal weight) allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; this is thus formative as well as summative assessment.