PHY3030 Quantum Physics II
2007-2008
Code: PHY3030
Title: Quantum Physics II
Instructors:
Prof. G.P. Srivastava
CATS credits: 10
ECTS credits: 5
Availability: unrestricted
Level: 3
Pre-requisites: N/A
Co-requisites: N/A
Background Assumed: N/A
Duration: Semester I
Directed Study Time: 22 lectures
Private Study Time: 78 hours
Assessment Tasks Time: -
Observation report: 2000/01 DAB
Aims
This module reviews the formal principles of Quantum Mechanics covered
in PHY2002 and then applies these principles to atomic
systems. The purpose of the applications chosen is to highlight the facets
of atomic systems and their quantum properties. They provide a view of
the basic features of atomic spectrosopy (and related magnetic effects) and
atomic structure as evidenced by the features of the periodic table.
Intended Learning Outcomes
Students should be able to:
Module Specific Skills
- use commutators mathematically in the solution of
eigenvalue problems and define a 'good' set of quantum numbers to
specify the physical state of a system,
- define the operator representing angular momentum and use it
to solve a wide range of problems,
- use perturbation theory to solve problems and interpret results,
- interpret experimental results which demonstrate the intrinsic
spin of an electron and be able to quote the properties of the intrinsic
spin operator,
- explain the origin of the un-coupled set of quantum numbers for the hydrogen
atom and the form of the associated eigenfunctions,
- describe the cirumstances where the coupled set of quantum
numbers is appropriate, particularly with respect to the optical
spectroscopy of sodium atoms (including circumstances where a magnetic
field is applied),
- construct eigenfunctions for systems of two identical
non-interacting particles when the particles are bosons or both fermions
and understand the significance of the Pauli-principle,
- explain the modifications needed to progress from the treatment of a
one-electron atom to that for a light multi-electron atom and of the
consequential electron configurations and ground states for the elements in
the periodic table.
Discipline Specific Skills
- discuss atomic physics and spectroscopy in an informed manner,
Personal and Key Skills
- construct arguments that explain observations,
- solve problems by using mathematics.
Learning and Teaching Methods
Lectures (22×1hr), problems classes (2×1hr) and tutorial support.
Assignments
Problems sheets.
Assessment
One 90-minute examination (100%).
Syllabus Plan and Content
- Review of Observables, Quantum Operators and their Properties [M1.5; R4.2-3]
- Angular Momentum
- Cartesian representation of angular momentum operators;
commutation relations involving position and
linear-momentum operators [M4.2; R5.1]
- Polar-coordinate representation of angular-momentum
operators [M4.2; R5.2]
- Eigenvalues of angular momentum [M4.2,4.5; R5.2]
- Rotational energy levels in diatomic molecules [M4.7]
- Hydrogen Atom
- The quantum numbers l and m in the eigenvalues of
angular momentum [M4.5; R5.2]
- Solution of the radial equation [M7.2; R3.4]
- Energy eigenvalues and the hydrogen-atom spectrum [M7.2; R3.4]
- Electron-density distributions [M7.2]
- Magnetic moments of atoms
- Magnetic dipole moment of orbital motion [M8.1-2; R5.3]
- Energy of and force on the atom in a magnetic field [M8.1-2]
- Stern-Gerlach experiment [M8.3; R5.3]
- Electron Spin
- Pauli interpretation [M10.4; R6.2]
- Spin quantum numbers [M8.3; R5.3]
- Anomalous spin magnetic moment [M8.3; R5.3]
- Landé g-factor [M8.3; R5.3]
- Atomic Structure
- Atomic quantum numbers [M7.2]
- Hydrogen-atom states [M7.2; R8.2]
- Vector coupling of angular momentum, total angular momentum [M6.3]
- Periodic table of elements [M7.3]
- Spectroscopic term notation
- Magnetic and Electric effects [M8.2, M8.4, M12.4; R6.5-6]
- Perturbation theory
- Optical transitions in atomic spectra
- Spin-orbit coupling, sodium D-lines
- Anomalous Zeeman effect in sodium
- Many-Particle Wavefunctions [M13.3-4; R10.3-4]
- Acceptable wave functions for two or more particles
- Symmetry and antisymmetry
- Bosons and fermions
- Exclusion principle for fermions, and condensation of bosons
- Singlet and triplet anti-symmetric wavefunctions for hydrogen molecule
Core Text
Rae A.I.M. (
2007),
Quantum Mechanics (
5th edition),
Chapman and Hal,
ISBN 1-584-88970-5 (UL:
530.12 RAE)
Supplementary Text(s)
McMurry S.M. (
1994),
Quantum Mechanics,
Addison Wesley,
ISBN 0-201-54439-3 (UL:
530.12 MCM)
Formative Mechanisms
This module is supported by the Stage 3 tutorials. Students
can also monitor their own progress with the example problems
which will be discussed in the problem classes.
Evaluation Mechanisms
The module will be evaluated using information gathered via the student representation mechanisms, the staff peer appraisal scheme, and measures of student attainment based on summative assessment.