MATH3111: QUANTUM MECHANICS III

• Analysis in Many Variables (MATH2031) and MathematicalPhysics II (MATH2071).

• None.

• Theoretical Physics 2 (PHYS2631) or Foundations of Physics3a (PHYS3621).

• To give an understanding of the reasons why quantum theory isrequired, to explain its basic formalism and how this can be applied tosimple situations, to show the power in quantum theory over a range ofphysical phenomena and to introduce students to some of the deepconceptual issues it raises.

• Problems with Classical Physics: Photo-electric effect, atomic spectra, wave-particle duality.
• Waves and the Schrodinger Equation.
• Formal Quantum Theory: Vectors, linear operators,hermitian operators, eigenvalues, complete sets, expectation values,commutation relations, Schrodinger representations.
• Applications in one-dimension.
• Angular Momentum: Commutation relations, eigenvalues,states, relation to spherical harmonics.
• Hydrogen Atom.
• Symmetry, Antisymmetry and ExclusionPrinciple.
• Conceptual Issues.
• Approximation Methods: Peturbation Theory.

Subject-specific Knowledge:

• By the end of the module students will: be able to solvenovel and/or complex problems in Quantum Mechanics.
• have a systematic and coherent understanding of theoreticalmathematics in the fields Quantum Mechanics.
• have acquired coherent body of knowledge of these subjectsdemonstrated through one or more of the following topic areas:Description of physical system in terms of state vectors.
• Description of observables using linear hermitianoperators.
• Schrodinger equation for time evolution of system.
• Representation of states and operators as wave functions anddifferential operators.
• Relating formal theory to experimentalmeasurements.
• Important examples including harmonic oscillator, 1D scattering and hydrogen atom.

Subject-specific Skills:

• In addition students will have specialised mathematicalskills in the following areas which can be used in minimal guidance:Modelling.

Key Skills:

• Lectures demonstrate what is required to be learned and theapplication of the theory to practical examples.
• Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge andunderstanding.
• Formatively assessed assignments provide practice in the application of logic and high level of rigour as well as feedback forthe students and the lecturer on students' progress.
• The end-of-year examination assesses the knowledge acquiredand the ability to solve predictable and unpredictableproblems.

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