Registry
Module Specifications
Archived Version 2011 - 2012
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Description To introduce the student to introductory 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 1. Demonstrate an understanding of how quantum states are described by wave functions; 2. Solve one-dimensional problems involving transmission, reflection and tunnelling of quantum probability amplitudes; 3. Explain the significance of operators and eigenvalue problems in quantum mechanics; 4. Identify and construct the wavefunction for the hydrogen atom and explain the significance of angular momentum operators in atomic physics. 5. Solve the Schrödinger equation and describe the properties of a single particle in one, two and three dimensional potentials 6. Apply first and second order perturbation theory to simple systems | |||||||||||||||||||||||||||||||||||||||||
All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml |
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Indicative Content and
Learning Activities THE TIME INDEPTNDENT SCHRODINGER EQUATIONSolution 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 THEORY: The Stern Gerlach Experiment, Spin, The Normal and Anomalous Zeeman effect.PERTURBATION THEORY: First Order Perturbation Theory, Variational Principle.THE TIME INDEPTNDENT SCHRODINGER EQUATIONSolution 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.PERTURBATION THEORY:First and Second Order Perturbation Theory, Variational Principle.ATOMIC THEORY:The Stern Gerlach Experiment, Spin, The Normal and Anomalous Zeeman effect. | |||||||||||||||||||||||||||||||||||||||||
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Indicative Reading List
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Other Resources None | |||||||||||||||||||||||||||||||||||||||||
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