GTPack is the free Mathematica group theory package. GTPack builds a bridge between computational algebra, university education and modern research. It has wide-ranging applications in condensed matter and solid-state physics, photonics, and quantum chemistry
Basic functionality: install point and space groups; calculate multiplication tables, classes, cosets, character tables, representation matrices, projection operators, Clebsch-Gordan coefficients, etc.
Structure: store, manipulate and generate structures of crystals and molecules; import/export to/from standard formats such as cif, POSCAR, etc.
Applications: construct Hamiltonians based on tight-binding, plane-wave expansion, crystal field theory; construct master equation for photonic crystals; calculate phonons based on harmonic approximation; analyze symmetry of electronic, photonic, phononic states; etc.
GTPack comes with a Mathematica-style documentation, an optional input validation, and guiding error messages and warnings.
GTPack allows for setting up and retrieving crystal and electronic structure databases (e.g. tight binding or crystal field parameters). We implement interfaces to investigate the output of standard software like ABINIT or VASP or the photonic band structure code MPB.
The application of GTPack is described in the book, Group Theory in Solid State Physics and Photonics: Problem Solving with Mathematica. Furthermore, we provide several tutorials to become familiar with the basic GTPack concepts.