PHY2020 : Principles of Quantum Mechanics
- Offered for Year: 2019/20
- Module Leader(s): Professor Nikolaos Proukakis
- Owning School: Mathematics, Statistics and Physics
- Teaching Location: Newcastle City Campus
|Semester 1 Credit Value:||10|
To discuss mathematically the wave theory of matter by analysing the Schrodinger equation and introduce basic operator algebra and quantum-mechanical postulates.
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.
|Scheduled Learning And Teaching Activities||Lecture||2||1:00||2:00||Revision lectures|
|Scheduled Learning And Teaching Activities||Lecture||6||1:00||6:00||Problem classes|
|Scheduled Learning And Teaching Activities||Lecture||22||1:00||22:00||Formal lectures|
|Guided Independent Study||Assessment preparation and completion||1||11:00||11:00||Revision for unseen Exam|
|Guided Independent Study||Assessment preparation and completion||1||1:30||1:30||Unseen Exam|
|Guided Independent Study||Assessment preparation and completion||5||5:00||25:00||Written assignments|
|Scheduled Learning And Teaching Activities||Drop-in/surgery||6||1:00||6:00||Drop-ins in lecture room|
|Scheduled Learning And Teaching Activities||Drop-in/surgery||12||0:10||2:00||Office hours|
|Guided Independent Study||Independent study||1||19:30||19:30||Studying, practising and gaining understanding of course material|
|Guided Independent Study||Independent study||5||1:00||5:00||Assignment review|
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 students’ 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 (two per week) provide an opportunity for more direct contact between individual students and the lecturer. A typical student might spend a total of one or two hours over the course of the module, either individually or as part of a group.
The format of resits will be determined by the Board of Examiners
|Prob solv exercises||1||M||10||N/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 assessment has a secondary formative purpose as well as a primary summative purpose.