(2024/2025) Quantum Physics

The notes are taken from the books required for the course:

• A. Berera and L.D. Debbio. Quantum Mechanics. Cambridge University Press, 2021.
• F. Ciccacci. Fondamenti di fisica atomica e quantistica. Edises, 2020.
• J.J. Sakurai and J. Napolitano. Modern Quantum Mechanics. Cambridge University Press, 2020.

You can view/download the PDF here. In the notes folder, you can also see the source code.

For any issue, use the appropriate section.

Course Syllabus

According to the official course syllabus:

• Quantum states
  • Introduction to quantum phenomena.
  • Measurements: intrinsic uncertainties.
  • Probability and probability density.
  • Quantum states.
  • Observables.
  • Pure and mixed states.
• Observables and operators
  • Hilbert space of quantum states.
  • Dirac notation: ket and bra.
  • Hermitian operators: eigenstates and eigenvalues.
  • Generalized statistical interpretation.
  • Commutators.
  • Heisenberg uncertainty principle.
  • Operators with discrete spectrum: matrix representation of operators and observables.
  • Continuous spectrum.
  • Complete basis sets.
  • Position representation and wave function.
  • Momentum representation and wave function in momentum space.
• Time evolution
  • Schrödinger equation.
  • Energy representation and stationary states.
  • Ehrenfest theorem and classical limit.
  • Quantum harmonic oscillator.
  • Creation and annihilation operators.
• Transformations
  • Unitary transformations.
  • Space translation and rotations.
  • Quantization of angular momentum.
  • Rising and lowering operators.
  • Electron spin, spinors and spin operators.
  • Pauli matrices.
• Composite systems
  • Identical particles.
  • Pauli exclusion principle for Fermions.
  • Singlet and triplet states.
  • Two level systems: qubits.
  • Entanglement.
  • Einstein-Podolsky-Rosen gedanken experiment.
  • Bell’s inequality.