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Module Title |
Quantum Physics II
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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:
- Solve Schrodingers equation for simple, 1D potentials.
- Solve the 2D and 3D infinite potential wells
- Solve simple tunnelling problems and give examples of tunnelling phenomena.
- 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.
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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 TIME INDEPTNDENT SCHRODINGER EQUATION:
Solution of one dimensional potential problems.
Simple 2D and 3D potentials.
The Harmonic Oscillator, Tunnelling.
Reflection and Transmission probabilities.
THE FORMAL RULES OF QUANTUM MECHANICS:
Introduction to Operators, Compatible observables, Commutation Relations, Orthogonality and expansion of wavefunction in basis sets.
Time Dependence.
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, and Spherical Co-ordinates, Particle in a 3-dimensional box. Particle on a ring, Particle on a Sphere, Central Potential, Hydrogen Atom, Many electron atoms.
ATOMIC PERTURBATION THEORY:
The Stern Gerlach Experiment, Spin, The Normal and Anomalous Zeeman effect.
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| Assessment | | Continuous Assessment | 30% | Examination Weight | 70% |
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Indicative Reading List
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1.Essential:
Introduction to Quantum Mechanics, A.C.Phillips
NonClassical Physics, Randy Harris
2.Supplementary:
Basic Quantum Mechanics J.L. Martin.
Quantum Mechanics A.I.M. Rae.
Quantum Mechanics F. Mandl
Quantum Mechanics S. McMurry.
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Programme or List of Programmes
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| AP | BSc in Applied Physics |
| BSSA | Study Abroad (DCU Business School) |
| BSSAO | Study Abroad (DCU Business School) |
| ECSA | Study Abroad (Engineering & Computing) |
| ECSAO | Study Abroad (Engineering & Computing) |
| HMSA | Study Abroad (Humanities & Soc Science) |
| HMSAO | Study Abroad (Humanities & Soc Science) |
| PF | BSc in Physics with French |
| PG | BSc in Physics with German |
| PHA | BSc in Physics with Astronomy |
| SHSA | Study Abroad (Science & Health) |
| SHSAO | Study Abroad (Science & Health) |
| Archives: | |
