Titlebook: ;

Intervention

Point Groups,, followed by an exploration of the so-called point groups of the first kind in Sect. .. In Sect. ., we investigate the types of point groups that can occur in solid-state physics before introducing the second kind of point groups in Sect. ..

陶瓷

Introvert

Quantum Mechanics and Group Theory,ugh the two more technical Sects. . and ., we want to start by pointing out the main goal of this chapter: As we will see in Sect. ., the eigenspaces of Hamiltonians are completely determined by group theory as far as their degeneracy and their symmetry properties are concerned.

ABYSS

Material Tensors and Tensor Operators,ensors (e.g. the magnetic susceptibility) are real numbers, while tensor operators are linear operators in a Hilbert space. Despite this significant difference, the group-theoretical analysis of both quantities is quite similar, which is why we treat them in a common chapter.

hermitage

Group Theory in Physics978-3-031-55268-7Series ISSN 2192-4791 Series E-ISSN 2192-4805

Consensus

happiness

Galactogogue

Arzneistoffmetabolismus (Biotransformation),This chapter centers on the crucial orthogonality theorems for irreducible representation matrices and their characters. We begin by proving the orthogonality theorem for representation matrices in Sect. .. Next, in Sect. ., we set up the orthogonality theorems for the characters.

Chagrin

MAIM

Neurotransmission und NeuromodulationIn this chapter, we focus on the Wigner-Eckart theorem, which allows us to calculate matrix elements of irreducible tensor components. In Sect. ., we first recall a common variant of this theorem that is usually covered in quantum mechanics courses. In this context, we also introduce the concept of Clebsch-Gordan coefficients.