  The lecture notes on "Many-body Quantum Dynamics with MCTDH-X," adapted from
the 2023 Heidelberg MCTDH Summer School, provide an in-depth exploration of the
Multiconfigurational Time-Dependent Hartree approach for indistinguishable
particles. They serve as a comprehensive guide for understanding and utilizing
the MCTDH-X software for both bosonic and fermionic systems. The tutorial
begins with an introduction to the MCTDH-X software, highlighting its
capability to handle various quantum systems, including those with internal
degrees of freedom and long-range interactions. The theoretical foundation is
then laid out on how to solve the time-dependent and time-independent
Schr\"odinger equations for many-body systems. The workflow section provides
practical instructions on setting up and executing simulations using MCTDH-X.
Detailed benchmarks against exact solutions are presented, showcasing the
accuracy and reliability of the software in ground-state and dynamic
simulations. The notes then delve into the dynamics of quantum systems,
covering relaxation processes, time evolution, and the analysis of propagation
for both bosonic and fermionic particles. The discussion includes the
interpretation of various physical quantities such as energy, density
distributions, and orbital occupations. Advanced features of MCTDH-X are also
explored in the last section, including the calculation of correlation
functions and the creation of visualizations through video tutorials. The notes
conclude with a Linux/UNIX command cheat sheet, facilitating ease of use for
users operating the software on different systems. Overall, these lecture notes
provide a valuable resource for researchers and students in the field of
quantum dynamics, offering both theoretical insights and practical guidance on
the use of MCTDH-X for studying complex many-body systems.
