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Module MAU34403: Quantum Mechanics I

Credit weighting (ECTS)
5 credits
Semester/term taught
Michaelmas term 2021-22
 
Contact Hours
11 weeks, 3 lectures including tutorials per week
Lecturer
Prof Sergey Frolov
Learning Outcomes
On successful completion of this module, students will be able to:
  • State the basic postulates of quantum mechanics;
  • Derive the general Schrödinger and Heisenberg equations of motion;
  • Apply quantum theoretical techniques to complex problems;
  • Demonstrate understanding-at and entry level-of 20th/21st century physics;
  • Solve problems in assigned and graded weekly problem sets;

Module Content
  • Mathematics of quantum mechanics: Bras and kets, Spin-1/2 representation of su(2), Hilbert spaces, Creation and annihilation operators, Hermitian operators, Tensor product, Coordinate representation and momentum representation of the Heisenberg algebra.
  • Postulates of quantum mechanics: States, Observables, Measurements, probabilities and amplitudes, Quantum dynamics, the Heisenberg picture and the Schrödinger picture, Symmetries in quantum mechanics.
  • Simple problems in various dimensions: Free particles,  Harmonic Oscillator, Bounded potential in one dimension, Scattering in one dimension, Separation of variables, The Pauli equation, Charged particle in a magnetic field, The Aharonov-Bohm effects.
  • Angular momentum and central field:  Irreducible representations of su(2),  Tensor product of irreducible representations, orbital angular momentum eigenfunctions, The radial Schrödinger equation,  Gross structure of hydrogen.
 
Module Prerequisite
MAU23402

Recommended Reading

• Shankar, Principles of Quantum Mechanics
• Sakurai, Modern Quantum Mechanics
• Binney and Skinner, The Physics of Quantum Mechanics
• Griffiths, Introduction to Quantum Mechanics
• Faddeev and Yakubovskii, Lectures on Quantum Mechanics for Mathematics Students
• Merzbacher, Quantum Mechanics

Assessment Detail
This module will be examined in a 2-hour examination in Michaelmas term. Continuous assessment will contribute 10% to the final grade for the module at the annual examination session. Re-assessments if required will consist of 100% exam.