MA225-6-SP-CO:
Quantum Mechanics

The details
2020/21
Mathematical Sciences
Colchester Campus
Spring
Undergraduate: Level 6
Current
Sunday 17 January 2021
Friday 26 March 2021
15
25 June 2020

 

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 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".

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.

Module aims

The module aims to provide students with a conceptual understanding of Quantum Mechanics, highlighting the break with "classical physics" concepts. Students will 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. Finally, they will develop problem-solving skills and learn how to apply learned techniques to unseen problems.

Module learning outcomes

On successful completion of this module, students should be able to:

a) Demonstrate systematic understanding of the basic principles of quantum mechanics and be able to apply them in simple physical situations.
b) Solve simple eigenfunction problems for Hermitian operators.
c) Calculate the quantum mechanical wave function, probability distribution in a given state.
d) Calculate quantum mechanical expectation values of observables. Predict how the state of an undisturbed quantum system evolves with time.
e) 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.
f) Apply key aspects of quantum mechanics in well-defined contexts, showing judgement in the selection and application of tools and techniques.
g) Gain knowledge and understanding of basic results about theory of linear operators in a Hilbert space.

Module information

Syllabus

1. Early quantum physics: quanta and particles. Bohr model of the hydrogen atom.
2. De Broglie waves.
3. The Schrodinger equation and the wave function.
4. The time-independent Schrodinger equation: potential barriers and potential wells.
5. Formalism of quantum mechanics: states and observables. Postulates of Quantum mechanics. Dirac bra- and ket- vectors. Hilbert space (non-rigorous treatment).
6. Expectation values and commutation relations.
7. Quantum harmonic oscillators. Raising and lowering operators.
8. Time evolution in Quantum Mechanics. Symmetries and conserved quantities. (examinable for level 6 students only)
9. Schrodinger versus Heisenberg (interaction) picture. (examinable for level 6 students only)

Learning and teaching methods

Teaching will be delivered in a way that blends face-to-face classes, for those students that can be present on campus, with a range of online lectures, teaching, learning and collaborative support.

Bibliography*

  • Griffiths, David J.; Schroeter, Darrell F. (2018) Introduction to quantum mechanics, Cambridge: Cambridge University Press.
  • Peleg, Yoav; Pnini, Reuven; Zaarur, Elyahu; Hecht, Eugene. (2010) Schaum's Outline of Quantum Mechanics, New York: McGraw-Hill Companies.
  • Haar, D. ter. (2014) Problems in quantum mechanics, Mineola: Dover Publications.
  • Greiner, Walter. (2001) Quantum mechanics: an introduction, Berlin: Springer.

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 Weighting
Coursework   Test     
Exam  120 minutes during Summer (Main Period) (Main) 

Overall assessment

Coursework Exam
20% 80%

Reassessment

Coursework Exam
20% 80%
Module supervisor and teaching staff
Dr Murat Akman, email: murat.akman@essex.ac.uk.
Dr Murat Akman
Dr Murat Akman (murat.akman@essex.ac.uk)

 

Availability
No
No
No

External examiner

Dr Tania Clare Dunning
The University of Kent
Reader in Applied Mathematics
Resources
Available via Moodle
Of 45 hours, 41 (91.1%) hours available to students:
4 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).

 

Further information
Mathematical Sciences

* Please note: due to differing publication schedules, items marked with an asterisk (*) base their information upon the previous academic year.

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