Principles of Quantum Mechanics(D)
PRINCIPLES OF QUANTUM MECHANICS (D)
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, Schr¨odinger 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
- S. Weinberg Lectures on Quantum Mechanics. CUP, 2nd ed., 2015
- J.J. Sakurai and J.J. Napolitano Modern Quantum Mechanics. CUP 2017
Associated GitHub page
https://jaircambridge.github.io/Principles-of-Quantum-Mechanics-D/