Undergraduate Course: Quantum Mechanics (PHYS09053)
Course Outline
| School | School of Physics and Astronomy |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 9 (Year 3 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 20 |
ECTS Credits | 10 |
| Summary | This two-semestered course covers fundamentals of quantum mechanics and its applications to atomic and molecular systems.
The first semester covers non-relativistic quantum mechanics, supplying the basic concepts and tools needed to understand the physics of atoms, molecules, and the solid state. One-dimensional wave mechanics is reviewed. The postulates and calculational rules of quantum mechanics are introduced, including Dirac notation. Angular momentum and spin are shown to be quantized, and the corresponding wave-function symmetries are discussed. The Schrodinger equation is solved for a number of important cases, including the harmonic oscillator and the Hydrogen atom. The fundamentals of time independent perturbation theory will be introduced as a means of approximating solutions to complex problems.
The second semester deals principally with atomic structure, the interaction between atoms and fields, and the atom- atom interactions in molecular physics. The course presents a detailed treatment of the hydrogen atom, including spin-orbit coupling, the fine structure, and the hyperfine interactions. Identical particles are reviewed in the context of electron electron interactions; applications include the Helium atom, Coulomb/exchange integrals, and alkali metals energy levels. Atom-field interactions are discussed, leading to dipole transitions, the Zeeman effect, the Lande g-factor, and the Stark effect. Finally atom-atom interactions are presented, leading to the study of molecular binding, molecular degrees of freedom (electronic, vibrational, and rotational), elementary group theory considerations and molecular spectroscopy. |
| Course description |
Quantum Mechanics (semester 1):
- Review and advanced application of wave mechanics to important potentials (Dirac well, harmonic potential, radial symmetric potentials)
- Applications to solving the required ordinary and partial differential equations (series expansion, applications of special functions, and separation of variables)
- Postulates of quantum mechanics and mathematical foundations
- Operator algebra including commutation relations and relation to matrix algebra and links to linear algebra techniques already developed previously
- Dirac notation and application linking to linear algebra
- Ladder operators introduced through revisiting the harmonic oscillator
- General angular momentum including operator algebra and application to spin as a special case; addition of angular momentum will be introduced
- Introduction to time independent perturbation theory as an application of the techniques introduced in semester 1
Quantum & Atomic Physics (semester 2):
- Time-independent perturbation theory for non-degenerate systems: the first-order formalism for energy eigenvalues and eigenstates. Higher order corrections outlined.
- Applications of perturbation theory: the ground state of helium, spin-orbit effects in hydrogen-like atoms.
- Non-degenerate time-independent perturbation theory: the first-order formulae for energy shifts and wavefunction mixing. Higher-orders.
- Time-independent perturbation theory for degenerate systems: the first-order calculation of energy shifts. Lifting of degeneracy by perturbations. Special cases.
- Hydrogen fine structure. Kinetic energy correction, spin-orbit correction and Darwin correction. Russell-Saunders notation, Zeeman effect, Stark effect, other atomic effects.
- Outline of multi-electron atoms and their treatment in the central field approximation. Slater determinants.
- The Rayleigh-Ritz variational method. Ground state of Hydrogen as an example. Result for Helium atom. Variational bounds for excited states.
- Self consistent field theory (Hartree), density functional theory. Many-particle wavefunction, exchange symmetry and correlations.
- The H2+ ion & molecular bonding. Born-Oppenheimer approximation. Variational estimates of the ground-state energy. Brief discussion of rotational and vibrational modes. Van der Waals force.
- Periodic potentials, reciprocal lattice, softening of band edge.
- Quantization of lattice vibrations (phonons). Linear chains.
- Time-dependent problems: time-dependent Hamiltonians, first-order perturbation theory, transition probabilities.
- Transitions induced by a constant perturbation: Fermi's Golden Rule. Harmonic perturbations and transitions to a group of states.
- Interaction of radiation with quantum systems. Electromagnetic radiation. Interaction with a 1-electron atom. The dipole approximation. Absorption and stimulated emission of radiation.
- Spontaneous emission of radiation. Einstein A and B coefficients. Electric dipole selection rules. Parity selection rules.
- Semiclassical approximation - WKB approximation.
- Quantum scattering theory. Differential and total cross-sections. The Born approximation via Fermi's Golden Rule. Density of states, incident flux, scattered flux. Differential cross-section for elastic scattering. Partial waves.
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Information for Visiting Students
| Pre-requisites | None |
| High Demand Course? |
Yes |
Course Delivery Information
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| Academic year 2015/16, Available to all students (SV1)
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Quota: None |
| Course Start |
Full Year |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
200
(
Lecture Hours 44,
Seminar/Tutorial Hours 44,
Formative Assessment Hours 3,
Revision Session Hours 1,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
104 )
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| Assessment (Further Info) |
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %
|
| Additional Information (Assessment) |
Coursework 20%
Examination 80% |
| Feedback |
Not entered |
| Exam Information |
| Exam Diet |
Paper Name |
Hours & Minutes |
|
| Main Exam Diet S2 (April/May) | Quantum Mechanics (PHYS09053) | 3:00 | |
Learning Outcomes
On completion of this course, the student will be able to:
- State the postulates and foundations of quantum mechanics
- Solve differential equations in related to quantum mechanical problems using techniques applied in this course (particularly series expansion, separation variables, and special functions)
- Understand and apply Dirac notation and operator algebra to problems in quantum mechanics and linear algebra
- Understand ladder operators and their properties
- Be able to apply generalised angular momentum techniques to problems and also have an understanding of the commutation relations and how to derive these
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Reading List
Albert Messiah, "Quantum Mechanics"
Claude Cohen Tannoudji, "Quantum Mechanics - vol 1"
L. D. Landau ad E. M. Lifshitz, "Quantum Mechanics: Non-Relativistic Theory" |
Additional Information
| Graduate Attributes and Skills |
Not entered |
| Special Arrangements |
None |
| Keywords | QMech |
Contacts
| Course organiser | Dr Christopher Stock
Tel: (0131 6)50 7066
Email: |
Course secretary | Mrs Siobhan Macinnes
Tel: (0131 6)51 3448
Email: |
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