Principles of Quantum Mechanics

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/