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MAU34403 Quantum mechanics I

Module Code MAU34403
Module Title Quantum mechanics I
Semester taught Semester 1
ECTS Credits 5
Module Lecturer Prof. Sergey Frolov
Module Prerequisites MAU23402 Advanced classical mechanics II

Assessment Details

  • This module is examined in a 2-hour examination at the end of Semester 1.
  • Continuous assessment contributes 10% towards the overall mark.
  • Any failed components are reassessed, if necessary, by an exam in the reassessment session.

Contact Hours

11 weeks of teaching with 3 lectures and 1 tutorial per week.

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.
  • Use symmetries to simplify complex problems.
  • Apply quantum theoretical techniques to complex problems.
  • Demonstrate an entry-level understanding of 20th and 21st century physics.

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, Pauli equation, charged particle in a magnetic field, Aharonov-Bohm effects.
  • Angular momentum and central field: Irreducible representations of su(2), tensor product of irreducible representations, orbital angular momentum eigenfunctions, radial Schrödinger equation, Gross structure of hydrogen.

Recommended Reading

  • Principles of quantum mechanics by Shankar.
  • Modern quantum mechanics by Sakurai.
  • The physics of quantum mechanics by Binney and Skinner.
  • Introduction to quantum mechanics by Griffiths.
  • Lectures on quantum mechanics for mathematics students by Faddeev and Yakubovskii.
  • Quantum mechanics by Merzbacher.