PHY2022 Quantum Mechanics I 2017-18
Dr A. Usher
 
Delivery Weeks: T1:01-11
Level: 5 (NQF)
Credits: 15 NICATS / 7.5 ECTS
Enrolment: 135 students (approx)

Description

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

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)

A student who has passed this module should be able to:

Syllabus Plan

  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

Description Study time KIS type
22×1-hour lectures 22 hours SLT
5×6-hour self-study packages 30 hours GIS
8×2-hour problems sets 16 hours GIS
Problems class support 8 hours SLT
Tutorial support 3 hours SLT
Reading, private study and revision 71 hours GIS

Assessment

Weight Form Size When ILOS assessed Feedback
0% Exercises set by tutor 3×1-hour sets (typical) Scheduled by tutor 1-12 Discussion in tutorials
0% Guided self-study 5×6-hour packages Fortnightly 1-12 Discussion in tutorials
10% 8 × Problems sets 2 hours per set Weekly 1-12 Marked in problems class, then discussed in tutorials
15% Mid-term test 30 minutes Weeks T1:06 1-11 Marked, then discussed in tutorials
75% Examination 120 minutes January 1-11 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:

ELE:

Further Information

Prior Knowledge Requirements

Pre-requisite Modules Mathematics for Physicists (PHY1026)
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%) 1-11 August/September assessment period

Notes: See Physics Assessment Conventions.

KIS Data Summary

Learning activities and teaching methods
SLT - scheduled learning & teaching activities 33 hrs
GIS - guided independent study 117 hrs
PLS - placement/study abroad 0 hrs
Total 150 hrs
Summative assessment
Coursework 10%
Written exams 90%
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
Availability unrestricted
Distance learning NO
Keywords Physics; Energy; Eigenvalues; Eigenstates; Hydrogen Atom; Observables; Particles; Perturbation theory; Quantum mechanics; Schrödinger equation; Time; Waves.
Created 01-Oct-10
Revised 01-Oct-11