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2010/1 Module Catalogue
 Module Code: PHY3006 Module Title: QUANTUM PHYSICS
Module Provider: Physics Short Name: PH3-QP
Level: HE3 Module Co-ordinator: ADAMS JM Dr (Physics)
Number of credits: 10 Number of ECTS credits: 5
 
Module Availability

Module Availability:

 

Semester 1

 

Assessment Pattern

Unit(s) of Assessment

 
Weighting Towards Module Mark( %)

 

Examination (End of semester)

 

100%

 

Qualifying Condition(s) 

 

University general regulations refer.

 
Module Overview

A Level HE3 module in the principles of quantum mechanics.  The course reviews quantum mechanics as a linear theory based on a series of fundamental postulates and develops the concepts of eigenfunction expansions, hydrogenic states, angular momentum operators, intrinsic spin and time-independent perturbation theory.

 
Prerequisites/Co-requisites

PHY2056 – Mathematical, Quantum and Computational Physics module.

 

Module Aims

To teach the basic principles of quantum mechanics and to apply these to a range of more advanced problems, such as the hydrogen atom, and to emphasise the power of matrix methods for many quantum mechanical systems.

 

Learning Outcomes

At the end of the module the student should understand the implications of the fundamental postulates of quantum mechanics.  Students should be able to apply matrix operator methods for suitable systems, including angular momentum, and interpret the properties of hydrogenic atoms.  Students should be able to apply the variational method and time-independent perturbation theory to suitable quantum-mechanical situations.

 

Module Content

Formalism of Quantum Mechanics

 

i.                 Formalism of Quantum Mechanics as a Linear Theory: probability interpretation of the wave function Y, normalisation;

 

ii.               Linear superposition, overlap integrals, vector interpretation and Dirac notation;

 

iii.              Observables and operators, measurements;

 

iv.             Eigenfunctions, eigenvalues, Hermitian operators, properties of eigenfunctions and eigenvalues of Hermitian operators;

 

v.               Expectation values;

 

vi.             Eigenfunction expansions and analogy with Fourier series, momentum eigenfunctions, orthogonality and completeness, physical meaning of expansion coefficients, commuting and compatible observables, Heisenberg's Uncertainty Principle;

 

vii.            The time-dependent Schrödinger equation.

 

 

Angular Momentum and Spin

 

i.                 Angular momentum operators and commutation relations;

 

ii.               Angular momentum eigenfunctions and eigenvalues, the magnetic and orbital angular momentum quantum numbers, spherical harmonics;

 

iii.              Matrix representation of operators, ladder operators;

 

iv.             Intrinsic spin, total angular momentum, addition of spin;

 

v.               The Stern-Gerlach experiment

 

 

The Hydrogenic Atom

 

i.                 Energy eigenfunctions for the hydrogenic atom;

 

ii.               Energy levels and quantum numbers, Pauli Exclusion Principle and general properties of hydrogenic atoms including orbital shapes and form of radial distribution function.

 

 

Approximation Methods

 

i.                Variational method and application to the simple harmonic oscillator;

 

ii.              Non-degenerate time-independent perturbation theory, first-order correction to the energy, first-order correction to the eigenfunctions and second-order correction to the energy;

 

iii.             Application to the hydrogen atom (gravitational effects, Zeeman effect, spin-orbit coupling and other perturbations);

 

Methods of Teaching/Learning

24 contact hours in lecture delivery format.           

 

Selected Texts/Journals

i.                S Gasiorowicz , Quantum Physics, John Wiley and Sons.

 

ii.              A Messiah, Quantum Mechanics, Dover.

 

iii.             P C W Davies and D S Betts , Quantum Mechanics, Chapman and Hall.

 

iv.            B H Bransden and C J Joachain, Introduction to Quantum Mechanics, Longman.

 

Last Updated

August 2010.