Principles of Quantum Mechanics 

Michaelmas Term, 24 Lectures – Dr E. Pajer 

Further information about this course is available on the Department of Mathematics course pages.

Examples papers are available on the DAMTP Examples page. 

1. Dirac formalism: Bra and ket notation, operators and observables, probability amplitudes, expectation values, complete commuting sets of operators, unitary operators. Schrodinger equation, wave functions in position and momentum space. [3] 

2. Time evolution operator: Schrodinger & Heisenberg pictures, Heisenberg equations of motion. [2] 

3. Harmonic oscillator: Analysis using annihilation, creation and number operators. Significance for normal modes in physical examples. [2] 

4. Multiparticle systems: Composite systems and tensor products, wave functions for multiparticle systems. Symmetry or antisymmetry of states for identical particles, Bose and Fermi statistics, Pauli exclusion principle. [3] 

5. Perturbation theory: Time-independent theory; second order without degeneracy, first order with degeneracy. [2] 

6. Angular momentum: Analysis of states ljm> from commutation relations. Addition of angular momenta, calculation of Clebsch-Gordan coefficients. Spin, Pauli matrices, singlet and triplet combinations for two spin half states. [4] 

7. Translations and rotations: Unitary operators corresponding to spatial translations, momenta as generators, conservation of momentum and translational invariance. Corresponding discussion for rotations. Reactions, parity, intrinsic parity. [3] 

8. Time-dependent perturbation theory: Interaction picture. First-order transition probability, the golden rule for transition rates. Application to atomic transitions, selection rules based on angular momentum and parity, absorption, stimulated and spontaneous emission of photons. [3] 

9. Quantum basics: Quantum data, qubits, no cloning theorem. Entanglement, pure and mixed states, density matrix. Classical determinism versus quantum probability, Bell inequality for singlet two-electron state, GHZ state. [2] 

Recommended Reading 

• E. Merzbacher Quantum Mechanics, 3rd edition. Wiley 1998 
• B.H. Bransden and C.J. Joachain Quantum Mechanics, 2nd edition. Pearson 
• J. Binney and D. Skinner The Physics of Quantum Mechanics. Cappella Archive, 3rd edition 
• P.A.M. Dirac The Principles of Quantum Mechanics. Oxford University Press 1967, reprinted 2003 
• S. Weinberg Lectures on Quantum Mechanics. CUP, 2nd ed., 2015 
• J.J. Sakurai and J.J. Napolitano Modern Quantum Mechanics. CUP 2017