MATH31120: Quantum Mechanics

• Analysis in Many Variables and Mathematical Physics

• None

• Advanced Quantum Theory

• To give an understanding of the reasons why quantum theory is required, to explain its basic formalism and how this can be applied to simple situations, to show the power in quantum theory over a range of physical phenomena and to introduce students to some of the deep conceptual 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 Exclusion Principle.
• Conceptual Issues.
• Approximation Methods: Peturbation Theory.

Subject-specific Knowledge:

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

Subject-specific Skills:

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

Key Skills:

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

Eight written or electronic assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students.

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