PHY3030 Quantum Physics II

2007-2008

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

1. Review of Observables, Quantum Operators and their Properties [M1.5; R4.2-3]
2. Angular Momentum
   1. Cartesian representation of angular momentum operators; commutation relations involving position and linear-momentum operators [M4.2; R5.1]
   2. Polar-coordinate representation of angular-momentum operators [M4.2; R5.2]
   3. Eigenvalues of angular momentum [M4.2,4.5; R5.2]
   4. Rotational energy levels in diatomic molecules [M4.7]
3. Hydrogen Atom
   1. The quantum numbers l and m in the eigenvalues of angular momentum [M4.5; R5.2]
   2. Solution of the radial equation [M7.2; R3.4]
   3. Energy eigenvalues and the hydrogen-atom spectrum [M7.2; R3.4]
   4. Electron-density distributions [M7.2]
4. Magnetic moments of atoms
   1. Magnetic dipole moment of orbital motion [M8.1-2; R5.3]
   2. Energy of and force on the atom in a magnetic field [M8.1-2]
   3. Stern-Gerlach experiment [M8.3; R5.3]
5. Electron Spin
   1. Pauli interpretation [M10.4; R6.2]
   2. Spin quantum numbers [M8.3; R5.3]
   3. Anomalous spin magnetic moment [M8.3; R5.3]
   4. Landé g-factor [M8.3; R5.3]
6. Atomic Structure
   1. Atomic quantum numbers [M7.2]
   2. Hydrogen-atom states [M7.2; R8.2]
   3. Vector coupling of angular momentum, total angular momentum [M6.3]
   4. Periodic table of elements [M7.3]
   5. Spectroscopic term notation
7. Magnetic and Electric effects [M8.2, M8.4, M12.4; R6.5-6]
   1. Perturbation theory
   2. Optical transitions in atomic spectra
   3. Spin-orbit coupling, sodium D-lines
   4. Anomalous Zeeman effect in sodium
8. Many-Particle Wavefunctions [M13.3-4; R10.3-4]
   1. Acceptable wave functions for two or more particles
   2. Symmetry and antisymmetry
   3. Bosons and fermions
   4. Exclusion principle for fermions, and condensation of bosons
   5. Singlet and triplet anti-symmetric wavefunctions for hydrogen molecule

Core Text

Supplementary Text(s)

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.