Problems and Solutions in Many-Body Quantum Theory

This practical guidebook provides a comprehensive set of exercises which illustrate the most relevant concepts in a first course on quantum many-body theory as part of advanced undergraduate or graduate courses. The problems come with detailed solutions which can easily be followed either by professors or students.

Bruno Julià-Díaz has been an associate professor in the Department of Quantum Physics and Astrophysics of the University of Barcelona since 2017. He obtained his PhD at the University of Salamanca in 2003, having subsequently carried out several post-doctoral stays at the University of Helsinki (2003-2004), the Atomique Energy Center (2004-2005) and the University of Pittsburgh (2005). He has been a Juan de la Cierva researcher (2006-2009) at the ICFO and a Ramón y Cajal researcher (2012-2017) at the UB. His research ranges from nuclear and hadron physics to ultra-cold gases and quantum multi-body physics. He has written one textbook on first year calculus and two popular books. Arnau Rios Huguet is a theoretical nuclear physicist, currently an associate professor at the University of Barcelona. Since the start of his scientific career in 2005, he has published over 50 refereed papers; supervised 5 PhD students; and has been awarded 3 individual fellowships to pursue his research interests. His work mainly focuses on nuclear many-body physics, using a variety of techniques that allow to tackle nuclear structure and dynamics problems and provide microscopic predictions for neutron-star physics. Dr Rios holds a PhD from the University of Barcelona (2007); was a postdoctoral research associate at Michigan State University (USA, 2007-2009); and a Marie Curie (2009-2011) and STFC Advanced Fellow (2011-2016) at the University of Surrey, where he was also a lecturer between 2015 and 2020. Héctor Briongos-Merino is a predoctoral researcher at the Universitat de Barcelona, where he began his doctoral studies in January 2024. He obtained his Bachelor's degree in Physics from the University of Valladolid in 2022, receiving the Extraordinary Award in Physics. Following this, he completed his Master's degree in Quantum Science and Technology at the University of Barcelona in 2023. His current research focuses on theoretical aspects of Atomtronics. His work specifically involves the study of ultracold dipolar bosons trapped in atomtronic circuits, exploring the unique properties and behaviors of these quantum systems which have significant implications for quantum simulation, precision measurements, and the exploration of novel quantum phenomena. Javier Rozalén Sarmiento is a predoctoral researcher at the Department of Quantum Physics and Astrophysics at the University of Barcelona. After finishing his Bachelor's studies in theoretical Physics and a Minor degree in Mathematics (University of Barcelona, 2021), he obtained a Master's degree in Quantum Science and Technology at the University of Barcelona in 2022. Since 2023, he is conducting a PhD in Nuclear Physics, leveraging the latest tools in the field of Artificial Intelligence for nuclear structure calculations. Artur Polls Martí (1952-2020) was a Professor of Physics at the University of Barcelona. He was a leading quantum many-body physicist, making significant contributions in the theoretical understanding of a variety of fields, including nuclear physics, quantum liquids and ultracold gases. Prof Polls was the author of over 200 refereed publications and supervised 10 PhD students. He started his career at the University of Barcelona, followed by a postdoctoral stint at the University of Tuebingen and a position at the University of Granada. Upon his return to Barcelona, he helped create an active community of researchers in quantum many-body physics that is extremely active at present.

1. Symmetries. 2. 2-body distribution function. 3. Fermions in 1-D. 4. Green's function. 5. Energy of the Free Fermi sea at T = 0. 6. Free Fermi sea at finite temperature. 7.Dynamic structure function. 8. Hartree-Fock. 9. Second quantization. 10. Density matrices.