Applied Mathematics
MP357: Quantum Mechanics II (5 ECTS)
(This course will be run every other year.) This is a continuation of MP356 and covers topics such as the 2-d and 3-d Schrodinger equation, spherically symmetric potentials, spherical harmonic functions, the hydrogen atom, angular momentum eigenstates, spin, spin-statistics, addition of angular momentum, rotations of a spinor, measurement in quantum mechanics, hidden variables and the Einstein- Podolsky-Rosen paradox, Bell's theorem.
Taught in Semester(s) II. Examined in Semester(s) II.
Workload: 36 hours (24 Lecture hours, 12 Tutorial hours).
Module Learning Outcomes.
On successful completion of this module the learner should be able to:
- Solve simple 2-d Schrodinger equation such as an infinite potential box or a 2-d harmonic oscillator.
- Solve simple spherically symmetric potential problems such as a spherical potential well.
- Compute eigenstates and eigenvalues of angular momentum and spin.
- Compute addition of angular momentum and spin eigenstates.
- Compute rotational transformations of a spinor.
- Prove Bell's theorem and demonstrate that hidden variables theory and quantum mechanics are incompatible.
Indicative Content
This is a follow on the the introductory course in quantum mechanics MP356.
Topics covered include:
(i) Introduction to the 2 and 3- d Schrodinger equation and wave functions. (ii) Spherically symmetric potentials and derivation of spherical harmonic functions. (iii) Derivation of the energy eigenvalues and eigenvectors for the hydrogen atom (iv) Angular momentum in quantum mechanics. Algebraic computation of the angular momentum eigenvalues and eigenvectors. Relationship to spherical harmonics. (v) Spin in quantum mechanics. Spinors and spin-statistics. (vi) Rotation of spinors. (vii) Measurement in quantum mechanics and hidden variables theory, the EPR paradox. (viii) Bell's theorem and inconsistency of hidden variables theory and quantum mechanics.
Module Resources
Introduction to Quantum Mechanics, David J. Griffiths, Pearson Education
Back