# 402-0209-00L Quantum Physics for Non-Physicists

Semester | Autumn Semester 2020 |

Lecturers | L. Pacheco Cañamero B. del Rio |

Periodicity | yearly recurring course |

Language of instruction | English |

Abstract | This course covers similar contents to Quantum Mechanics I, but through an information-theoretical approach, especially suited for students with backgrounds in computer science, mathematics or engineering. We start from the postulates of quantum theory and build up to the tools needed to study the behaviour of complex systems, from entangled spins to the hydrogen atom and nano heat engines. |

Objective | This course teaches the formalism and physics of quantum mechanics. Students are equipped with tools to analyse complex settings such as the hydrogen atom, thermal engines and scattering. It covers similar contents to QM1 but from an information-theoretical perspective. |

Content | 1. Quantum formalism, from qubits to particles in space - Dirac notation - Postulates of quantum physics - Discrete systems: qubits, the Bloch sphere - Continuous variables: position and momentum, the wave function - Multiple systems: tensor product, entanglement - Application: internal degrees of freedom of photons and electrons 2. Time and dynamics for quantum systems - Unitary evolution and the Schrödinger equation - Hamiltonian evolution and functions of operators - Commutation relations and symmetries - Application: the double-slit experiment 3. Uncertainty and open systems - Modelling uncertainty: the density matrix - Example: thermal states - Open systems, irreversible evolution and Lindblad operators - Application: heat engines 4. Spin and oscillators - Spin and rotation - Orbital angular momentum - Ladder systems and the harmonic oscillator 5. Several particles, bosons and fermions - Relative coordinates - Identical particles and symmetry groups - Fermions and bosons - Second quantization 6. Problems in 1D - Dynamics of a free particle - Potential wells and stationary waves - Spin chains 7. Problems in 3D - Central potentials - The hydrogen atom 8. Perturbation theory - Assumptions and derivation - Application: scattering 9. Non-locality - Bell's theorem - Non-classicality of quantum theory (extra) - Modular momentum (extra) 10. Foundations of quantum theory - Paradoxes - Quantum reference frames - Deriving the postulates of quantum mechanics from first principles |

Lecture notes | Lecture notes will be distributed through the semester. |

Literature | Quantum Processes Systems, and Information, by Benjamin Schumacher and Michael Westmoreland, available at Link |

Prerequisites / Notice | This course is an alternative to Quantum Mechanics I aimed primarily at non-physicists, and in particular at students with a background in computer science, mathematics or engineering. Basic linear algebra and calculus knowledge is required (equivalent to first-year courses). Basic physics knowledge (equivalent to first-year courses) is recommended but not strictly necessary. Note that while we follow an information-theoretical approach, this is not a course on quantum information theory or quantum computing. It therefore complements those courses offered at ETH in both semesters. |