Advanced Quantum Physics

URL study guide

https://tue.osiris-student.nl/onderwijscatalogus/extern/cursus?cursuscode=32AQP&collegejaar=2025&taal=en

Omschrijving

General subjects and skills

• Dirac notation

Spin and angular momentum

• Addition of spins
• Addition of general angular momenta
• Clebsch-Gordan coefficients
• Spin triplets and singlets
• Stern-Gerlach experiment
• Gyromagnetic ratio
• Larmor precession

Identical particles and interactions

• Bosons and fermions
• Pauli exclusion principle
• Exchange force
• Covalent chemical bond

Atomic structure and behavior

• Orthohelium and parahelium
• Filling of atomic (sub)shells
• Electron configuration and spectroscopic notation
• Periodic table
• Hund’s rules

Solids and electronic structure

• 3D free electron gas
• Fermi energy/sphere
• Degeneracy pressure
• Band structure of 1D Dirac comb
• Band structures
• Metals, insulators, semiconductors

Time-independent perturbation theory

• Non-degenerate perturbation theory
• Degenerate perturbation theory
• Good states theorem
• Scalar relativistic correction for H
• Spin-orbit coupling
• Fine structure for H
• Zeeman effect: strong, weak, intermediate field
• Landé g-factor

Variational principle and applications

• Application to He: screening of nuclear charge
• Application to H₂⁺
• Application to H₂: covalent chemical bond

Time-dependent perturbation theory

• Emission and absorption of radiation
• Working principle of the laser
• Rabi oscillations
• Incoherent perturbations
• Spontaneous emission
• Einstein’s A and B coefficients
• Spontaneous emission
• Excited state lifetimes
• Selection rules
• Fermi’s golden rule

Modern applications

• EPR paradox
• Bell’s theorem
• Quantum information theory
• Organic light-emitting diodes

Computational tools and skills

• Using Mathematica

Mathematical concepts and tools

• Linear algebra
  • Basic matrix operations
  • Vector spaces

Doelstellingen

After the end of this course, you (the student) will be able to:

1. Understand and apply the basic concepts in quantum physics (e.g. the Schrodinger equation, observables, Copenhagen interpretation, spin, coupling of angular momenta, etc.).
2. Understand and apply the formalism of quantum physics in mathematical language, in particular that of linear algebra, to describe wave functions, operators, measurements, and expectation values.
3. Understand the importance of different symmetries in quantum physics (e.g. spatial symmetries, spin symmetries, exchange symmetries for indistinguishable particles).
4. Explain and analyze important physical effects following from quantum physics, e.g. the Pauli principle, exchange force, covalent chemical bond, structure of the periodic table, Fermi energy, band structure of solids, selection rules, etc..
5. Describe and analyze the effect of external electromagnetic fields applied to single- or few-particle quantum systems (e.g. Larmor precession, Zeeman splitting, light absorption and emission).
6. Apply standard approximate methods such as perturbation theory and the variational principle to selected quantum physical problems.
7. Solve and analyze selected quantum physical problems (e.g. problems related to the harmonic oscillator, infinite square well, small atoms, time-independent and time-dependent perturbations) both analytically and numerically in Mathematica.
8. Recognize the importance of quantum physics in contemporary applications such as quantum technology and photonics.

Beoordelingsmethode

Written examination