Institute of Astronomy

Part II Principles of Quantum Mechanics

Michaelmas Term, 24 Lectures – Dr D Skinner

PRINCIPLES OF QUANTUM MECHANICS                                             24 lectures, Michaelmas Term
IB Quantum Mechanics is essential.

Dirac formalism
Bra and ket notation, operators and observables, probability amplitudes, expectation values, complete commuting sets of operators, unitary operators. Schr¨odinger equation, wave functions in position and momentum space. [3]
Time evolution operator, Schroedinger and Heisenberg pictures, Heisenberg equations of motion. [2]

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

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]

Perturbation theory

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

Angular momentum
Analysis of states |jmi 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]

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

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]

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]

Appropriate books
† 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
C.J. Isham Lectures on Quantum Theory: Mathematical and Structural Foundations. Imperial College
Press 1995

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