MA225-6-SP-CO:
Quantum Mechanics

The details
2023/24
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Spring
Undergraduate: Level 6
Current
Monday 15 January 2024
Friday 22 March 2024
15
04 January 2024

 

Requisites for this module
MA105 and MA222
(none)
MA201 or MA202 or MA210
(none)

 

(none)

Key module for

BSC G1F3 Mathematics with Physics,
BSC G1F4 Mathematics with Physics (Including Placement Year),
BSC G1F5 Mathematics with Physics (Including Foundation Year),
BSC GCF3 Mathematics with Physics (Including Year Abroad)

Module description

Quantum Mechanics has been at the root of the enormous advances and major discoveries in Physics over the last century, having strong influence on the development of modern technology, like lasers, transistors and superconductors.


It gives a description of nature that is very different from the one of Classical Mechanics, in particular being non-deterministic and "non-local", and seeming to give a crucial role to the presence of "observers"

Module aims

The aims of this module are:



  • to provide students with a conceptual understanding of Quantum Mechanics, highlighting the break with "classical physics" concepts.

  • to learn a fundamental theory describing the physical world through combining their mathematical skills learned in earlier stages. Through lectures, classes and seminars, students will develop graduate skills, like ability to assimilate, process and engage with new material quickly and efficiently.

  • to develop problem-solving skills and learn how to apply learned techniques to unseen problems.

Module learning outcomes

By the end of the module, students will be expected to be able to:



  1. Demonstrate systematic understanding of the basic principles of quantum mechanics and be able to apply them in simple physical situations.

  2. Solve simple eigenfunction problems for Hermitian operators.

  3. Calculate the quantum mechanical wave function, probability distribution in a given state.

  4. Calculate quantum mechanical expectation values of observables. Predict how the state of an undisturbed quantum system evolves with time.

  5. Demonstrate the capability accurately to analyse and solve problems using a reasonable level of skill in in the following areas: potential wells and barriers in one dimension and the treatment of eigenvalue problems in quantum mechanics.

  6. Apply key aspects of quantum mechanics in well-defined contexts, showing judgement in the selection and application of tools and techniques.

  7. Gain knowledge and understanding of basic results about theory of linear operators in a Hilbert space.

Module information

The module begins with a brief historical and conceptual introduction, explaining the reasons for the failure of classical ideas, and the corresponding changes needed to describe the physical world. Then it presents the Schrodinger picture in Quantum mechanics.


Indicative syllabus


Early quantum physics: quanta and particles. Bohr model of the hydrogen atom.


De Broglie waves.


The Schrodinger equation and the wave function.


The time-independent Schrodinger equation: potential barriers and potential wells.


Formalism of quantum mechanics: states and observables. Postulates of Quantum mechanics. Dirac bra- and ket- vectors. Hilbert space (non-rigorous treatment).


Expectation values and commutation relations.


Quantum harmonic oscillators. Raising and lowering operators.


Time evolution in Quantum Mechanics. Symmetries and conserved quantities.


Schrodinger versus Heisenberg (interaction) picture.

Learning and teaching methods

Teaching in the School will be delivered using a range of face-to-face lectures, classes, and lab sessions as appropriate for each module. Modules may also include online only sessions where it is advantageous, for example for pedagogical reasons, to do so.

Bibliography

The above list is indicative of the essential reading for the course.
The library makes provision for all reading list items, with digital provision where possible, and these resources are shared between students.
Further reading can be obtained from this module's reading list.

Assessment items, weightings and deadlines

Coursework / exam Description Deadline Coursework weighting
Coursework   Test     
Exam  Main exam: In-Person, Closed Book, 120 minutes during Summer (Main Period) 
Exam  Reassessment Main exam: In-Person, Closed Book, 120 minutes during September (Reassessment Period) 

Additional coursework information

Reassessment strategy

If a student fails the test and the exam they will only take the resit exam which will be worth 100%;
If a student fails the exam but passes the test they will only take the resit exam, the mark for which will be re-aggregated with the test mark;
If a student fails the test but passes the exam they will take the resit test, the mark for which will be re-aggregated with the exam mark.

Exam format definitions

  • Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
  • In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
  • In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
  • In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary, for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.

Your department will provide further guidance before your exams.

Overall assessment

Coursework Exam
20% 80%

Reassessment

Coursework Exam
20% 80%
Module supervisor and teaching staff
Dr Georgi Grahovski, email: gggrah@essex.ac.uk.
Dr Georgi Grahovski
maths@essex.ac.uk

 

Availability
No
No
No

External examiner

Prof Stephen Langdon
Brunel University London
Professor
Resources
Available via Moodle
Of 20 hours, 0 (0%) hours available to students:
0 hours not recorded due to service coverage or fault;
20 hours not recorded due to opt-out by lecturer(s), module, or event type.

 

Further information

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