MODULE TITLE

Quantum Mechanics I

 

CREDIT VALUE

15

MODULE CODE

PHY2022

MODULE CONVENER

Dr A. Usher

 

 

DURATION

TERM

1

2

3

Number Students Taking Module (anticipated)

170

WEEKS

T1:01-11

 

DESCRIPTION – summary of the module content (100 words)

This module introduces the mathematical expression of the basic principles of quantum mechanics and methods for finding solutions of problems that permit straightforward mathematical analysis. These solutions demonstrate many of the general features of the subject and will be applied in subsequent modules in the Physics programme.

MODULE AIMS – intentions of the module

Quantum Mechanics is one of the fundamental building-blocks of Physics. It affects profoundly the way we think about the universe and is the basis for much of condensed-matter, nuclear and statistical physics. It also has a strong influence on technological developments, for instance in optical and electronic devices. This module aims to give students a firm grounding in the subject and to prepare them for future modules such as PHY3052 Nuclear and High-Energy Particle Physics.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

 On successful completion of this module you should be able to:

Module Specific Skills and Knowledge:

  1. describe the definition and interpretation of the wavefunction and of operators in quantum mechanics;
  2. discuss the origin of energy quantisation and quantum tunnelling effects;
  3. describe the general properties of the stationary states of quantum particles confined to simple symmetric potentials;
  4. perform calculations on wavefunctions, and solve the Schrödinger equation for a range of problems;
  5. use time-independent perturbation theory to solve problems and interpret results;
  6. explain the origin of the un-coupled set of quantum numbers for the hydrogen atom and the form of the associated eigenfunctions;

Discipline Specific Skills and Knowledge:

  1. use the principles of quantum mechanics to solve problems;
  2. explain quantum mechanics to a lay-person in an informed manner;

Personal and Key Transferable / Employment Skills and Knowledge:

  1. construct arguments that explain observations;
  2. solve problems by using mathematics;
  3. use a range of resources to develop an understanding of topics through independent study.
  4. meet deadlines for completion of work for problems classes and develop appropriate time-management strategies.

SYLLABUS PLAN – summary of the structure and academic content of the module

  1. Introduction
    Brief historical survey; recap of PHY1022; what is required of the theory; the wave equation; time-dependent Schrödinger equation
  2. Wave Functions and their Interpretation
    The Born probability interpretation; normalization of the wave function; first postulate; wave function of a free particle; wave function of a confined particle; Gaussian wave packets (Self-study pack): the uncertainty principle; time evolution of wave packets
  3. Dynamical Variables
    Observables as operators; the second postulate; the third postulate; physical significance of eigenfunctions; Schrödinger equation revisited
  4. Stationary States and the Time-Independent Schrödinger Equation
    Time-independent probability distributions; the time-independent Schrödinger equation; stationary states: eigenfunctions of the Hamiltonian; example: region of constant potential; method of solution ; boundary conditions
  5. Particle in a Box - the Infinite Square Well
    Internal solution; boundary conditions; energy quantization; normalized wave functions
  6. The Finite Square Potential Well (Self-study pack)
    Interior and exterior solutions; boundary conditions; symmetric solutions - energies and wave functions; antisymmetric solutions - energies and wave functions
  7. Flow of Particles
    Probability flux; continuity equation; persistence of normalization; derivation of probability flux
  8. Barrier Problems
    Boundary conditions at a potential discontinuity; a potential step; tunnelling: reflection and transmission by a barrier; practical examples of tunnelling
  9. Quantum Measurement and the Structure of Quantum Mechanics
    Properties of Hermitian operators; the superposition principle: fourth postulate; measurements of a general quantum state; commutation relations and simultaneous observables; the uncertainty principle; commutation with the Hamiltonian; summary: the postulates of quantum mechanics
  10. The Quantum Harmonic Oscillator
    Hamiltonian in operator form; ladder operators; eigenvalues and eigenfunctions
  11. The 3D Time-Independent Schrödinger Equation
    Momentum eigenfunctions in 3D; Schrödinger equation in 3D Cartesian coordinates (Self-study pack); example: particle in a 3D box; Schrödinger equation in spherical polar coordinates
  12. Angular Momentum
    Cartesian representation of angular momentum operators; commutation relations; polar representation of angular momentum operators; eigenfunctions and eigenvalues; example: Rotational energy levels of a diatomic molecule
  13. The Hydrogen Atom
    Solutions of the angular equation; solutions of the radial equation; energy eigenvalues - the hydrogen spectrum; electron density distributions
  14. First-Order Time-Independent Perturbation Theory
    Perturbation theory for non-degenerate levels; perturbation theory for degenerate levels

 

LEARNING AND TEACHING

 

LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)

Scheduled Learning & Teaching activities  

33 hours

Guided independent study  

117 hours

Placement/study abroad

0 hours

 

DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS

 Category 

 Hours of study time 

 Description 

Scheduled Learning & Teaching activities

22 hours

22×1-hour lectures

Guided independent study

30 hours

5×6-hour self-study packages

Guided independent study

16 hours

8×2-hour problems sets

Scheduled Learning & Teaching activities

8 hours

Problems class support

Scheduled Learning & Teaching activities

3 hours

Tutorial support

Guided independent study

71 hours

Reading, private study and revision

 

ASSESSMENT

 

 FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade

Form of Assessment

Size of the assessment e.g. duration/length

ILOs assessed

Feedback method

Exercises set by tutor

3×1-hour sets (typical)

1-12

Discussion in tutorials

Guided self-study

5×6-hour packages

1-12

Discussion in tutorials

SUMMATIVE ASSESSMENT (% of credit)

Coursework

10%

Written exams

90%

Practical exams

0%

 

DETAILS OF SUMMATIVE ASSESSMENT

Form of Assessment

 

% of credit

Size of the assessment e.g. duration/length

 ILOs assessed 

Feedback method

8 × Problems sets

10%

2 hours per set

1-12

Marked in problems class, then discussed in tutorials

Mid-term test

15%

30 minutes

1-11

Marked, then discussed in tutorials

Examination

75%

120 minutes

1-11

Mark via MyExeter, collective feedback via ELE and solutions.

 DETAILS OF RE-ASSESSMENT (where 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%)

1-11

August/September assessment period

RE-ASSESSMENT NOTES  

See Physics Assessment Conventions.

 

RESOURCES

 

 INDICATIVE LEARNING RESOURCES -  The following list is offered as an indication of the type & level of information that you are expected to consult. Further guidance will be provided by the Module Convener.

Core text:

Supplementary texts:

ELE:

CREDIT VALUE

15

ECTS VALUE

7.5

PRE-REQUISITE MODULES

Mathematics for Physicists (PHY1026)

CO-REQUISITE MODULES

none

NQF LEVEL (FHEQ)

5

AVAILABLE AS DISTANCE LEARNING

NO

ORIGIN DATE

01-Oct-10

LAST REVISION DATE

01-Oct-11

KEY WORDS SEARCH

Physics; Energy; Eigenvalues; Eigenstates; Hydrogen Atom; Observables; Particles; Perturbation theory; Quantum mechanics; Schrödinger equation; Time; Waves.

Module Descriptor Template Revised October 2011