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Module Title |
Quantum Physics 2
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Module Code |
PS301
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School |
School of Physical Sciences
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Online Module Resources
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| Module Co-ordinator | Dr Tony Cafolla | Office Number | N141 |
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Level |
3
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Credit Rating |
5
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Pre-requisite |
None
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Co-requisite |
None
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Module Aims
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To introduce the student to more advanced topics in quantum mechanics. The formal rules of quantum mechanics are introduced. It is shown how observable quantities such as position, momentum and angular momentum are represented by operators. The properties of these operators are studied. The angular momentum operators are studied in detail leading to a series of applications of the wave equation to 1-, 2- and 3- dimensional physical systems. Emphasis is placed on the central potential and the energy and angular momentum properties of the Hydrogen atom are studied. Simple perturbation methods for solving non-trivial problems are introduced and applications of these methods to atomic and molecular systems are examined.
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Learning Outcomes
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After studying the material in this course the student should be able to:
- State and understand the formal rules of quantum mechanics
- Expand a wave function in terms of a basis set of functions and interpret the expansion coefficients in terms of measurement probabilities
- Understand the significance of Commutators in terms of the compatibility of measurements and to be able to perform simple commutator algebra.
- Derive operators for the angular momentum components LX, LY, LZ and L2 in terms of position and momentum operators in carthesian and spherical co-ordinates. Understand the rules for the coupling of angular momenta.
- Describe and interpret the wave-functions of the hydrogen atom; understand the origin and interpretation of the quantum numbers n,l and m in the context of a central potential.
- Solve the time independent Schrodinger equation for three dimensional potentials.
- Apply the Variational principle and first and second order perturbation theory.
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Indicative Time Allowances
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Hours
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Lectures |
24
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Tutorials |
6
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Laboratories |
0
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Seminars |
0
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Independent Learning Time |
45
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Total |
75
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Placements |
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Assignments |
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NOTE
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Assume that a 5 credit module load represents approximately 75 hours' work, which includes all teaching, in-course assignments, laboratory work or other specialised training and an estimated private learning time associated with the module.
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Indicative Syllabus
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THE FORMAL RULES OF QUANTUM MECHANICS:
Introduction to Operators, Compatible observables, Commutation Relations, Orthogonality and expansion of
wavefunction in basis sets. Symmetry and Conservation laws.
ANGULAR MOMENTUM:
Angular momentum operators, eigenvalues and eigenvectors. The rigid rotor, Spin, Addition of angular
momenta, Spin-orbit coupling, L-S and JJ coupling.
THREE DIMENSIONAL SCHRODINGER EQUATION:
Separation in Cartesian, Spherical and Cylindrical Co-ordinates, Particle in a 3-dimensional box. Radial
Square Well, 3-dimensional harmonic oscillator. Central Potential, Hydrogen Atom, Many electron atoms,
Molecular rotations and vibrations.
PERTURBATION THEORY:
Non-degenerate and degenerate perturbation theory with applications. The Zeeman and Paschen-Back
effects. The Variational Principle. Time Dependent Perturbation Theory, Fermi's Golden Rule.
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| Assessment | | Continuous Assessment | 30% | Examination Weight | 70% |
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Indicative Reading List
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1. Basic Quantum Mechanics J.L. Martin.
2. Quantum Mechanics A.I.M. Rae.
3. Quantum Mechanics F. Mand.l
4. Quantum Mechanics S. McMurry.
5. Introduction to Quantum Mechanics, A.C.Phillips.
6. NonClassical Physics, Randy Harris
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Programme or List of Programmes
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| AP | BSc in Applied Physics |
| PF | BSc in Physics with French |
| PG | BSc in Physics with German |
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