PHYM002 |
Quantum Mechanics II |
2013-14 |
|
Dr A.V. Shytov |
|
|
Delivery Weeks: |
T1:01-11 |
|
Level: |
7 (NQF) |
|
Credits: |
15 NICATS / 7.5 ECTS |
|
Enrolment: |
48 students (approx) |
|
Description
The module covers a range of more advanced topics leading to the discussion of
quantum transitions and non-relativistic scattering. Much of physics concerns
manifestations of the electromagnetic interaction which is susceptible to
perturbation techniques. The methods outlined in the module are applicable to
many situations in condensed matter and nuclear physics enabling useful and
informative solutions to be obtained to non-exactly-soluble problems without
resort to numerical methods.
Module Aims
The aim of this module is to build upon the foundations laid in
PHY2022 Quantum Mechanics I and
develop the students' grasp of quantum mechanics - particularly its formalism and applications
- to the point where they will be able to engage with contemporary research literature.
Intended Learning Outcomes (ILOs)
A student who has passed this module should be able to:
-
Module Specific Skills and Knowledge:
- formulate, and evaluate, the solutions to a variety of perturbed
quantum mechanical systems;
- calculate energy shifts, transition probabilities
(and rates) and cross-sections;
-
Discipline Specific Skills and Knowledge:
- use Dirac notation;
- use mathematics to solve problems;
- present and defend their solutions to problems to the group;
-
Personal and Key Transferable / Employment Skills and Knowledge:
- undertake co-operative learning by discussing the contents of the module
amongst themselves;
- make informal presentations of technical material;
- work independently in order to meet deadlines.
Syllabus Plan
-
Dirac Notation
-
Non-degenerate Perturbation Theory
- Introduction
- Mathematical basis
- Perturbation method
- Sequence of perturbation equations
- Solution of first-order equation
- First-order result for change to energies and
wavefunctions
- Second-order energy shifts
- Anharmonic oscillator
- Finite-nucleus correction
-
Degenerate Perturbation Theory
- Introduction
- "Almost degenerate" limit of nondegenerate perturbation theory
- Solution of the problem of a doubly degenerate state
- Stark effect
-
Quantum Transitions
- Introduction
- Time-dependent perturbation theory
- First-order theory
- Constant perturbation from t = 0
- Energy conservation
- Transition rate, Fermi's golden rule
- Harmonic perturbation and induced energy changes to a
quantum system
-
Two-particle Systems
- Noninteracting particles
- Helium atom
- Exchange interaction
- Spin eigenvalues and eigenfunctions for two electrons
- Spin wave functions and interchange symmetry
- Hydrogen molecule
-
Many-particle Systems
-
Nonrelativistic scattering theory
- Incident and scattered waves
- Integral equation
- Scattering amplitude
- Phase shifts
- Differential cross section
- Total cross section
- Born approximation
- Introduction to quantum information
Learning and Teaching
Learning Activities and Teaching Methods
Description |
Study time |
KIS type |
20×1-hour lectures |
20 hours
|
SLT |
2×1-hour problems/revision classes |
2 hours
|
SLT |
5×6-hour self-study packages |
30 hours
|
GIS |
4×4-hour problem sets |
16 hours
|
GIS |
Reading, private study and revision |
82 hours
|
GIS |
Assessment
Weight |
Form |
Size |
When |
ILOS assessed |
Feedback |
0% |
Guided self-study |
5×6-hour packages |
Fortnightly |
1-8 |
Discussion in class |
0% |
4 × Problems sets |
4 hours per set |
Fortnightly |
1-8 |
Solutions discussed in problems classes. |
100% |
Final Examination |
2 hours 30 minutes |
January |
1-8 |
Mark via MyExeter, collective feedback via ELE and solutions. |
Resources
The following list is offered as an indication of the type & level of information that
students are expected to consult. Further guidance will be provided by the Module Instructor(s).
Core text:
Supplementary texts:
-
Open University Science Foundation Course Team (1988), Quantum Mechanics: An introduction, Open University (UL: 500 OPE/X)
-
Open University SM355 Course Team (1986), Quantum Mechanics: Units 12-14, Open University (UL: 530.12 OPE/X)
-
Open University SM355 Course Team (1986), Quantum Mechanics: Units 15-16, Open University (UL: 530.12 OPE/X)
-
Park D. (1974), Introduction to the Quantum Theory (2nd edition), McGraw-Hill (UL: 530.12 PAR)
-
Pauling L. and Wilson E.B. (1935), Introduction to Quantum Mechanics, McGraw-Hill (UL: 530.12 PAU)
-
Rae A.I.M. (2007), Quantum Mechanics (5th edition), Chapman and Hal, ISBN 1-584-88970-5 (UL: 530.12 RAE)
ELE:
Further Information
Prior Knowledge Requirements
Pre-requisite Modules |
Quantum Mechanics I (PHY2022) and Mathematics with Physical Applications (PHY2025) |
Co-requisite Modules |
none |
Re-assessment
Re-assessment is not available except when required by referral or deferral.
Original form of assessment |
Form of re-assessment |
ILOs re-assessed |
Time scale for re-assessment |
Whole module |
Written examination (100%) |
1-8 |
August/September assessment period |
Notes: See Physics Assessment Conventions.
KIS Data Summary
Learning activities and teaching methods |
SLT - scheduled learning & teaching activities |
22 hrs |
GIS - guided independent study |
128 hrs |
PLS - placement/study abroad |
0 hrs |
Total |
150 hrs |
|
|
Summative assessment |
Coursework |
0% |
Written exams |
100% |
Practical exams |
0% |
Total |
100% |
|
Miscellaneous
IoP Accreditation Checklist |
- QM-05 Wave function and its interpretation
- QM-06 Standard solutions and quantum numbers to the level of the hydrogen atom
- QM-07 Tunnelling
- QM-08 First order time independent perturbation theory
- QM-09 Quantum structure and spectra of simple atoms
- QM-12 Pauli exclusion principle, fermions and bosons and elementary particles
|
Availability |
MPhys and PGRS only |
Distance learning |
NO |
Keywords |
Physics; Dirac notation; Energy; Eigenvalues; Eigenstates; Helium Atom; Observables; Particles;
Perturbation theory; Quantum mechanics; Schrödinger equation; Scattering theory; Time; Waves. |
Created |
01-Oct-10 |
Revised |
11-Sep-13 |