Group Theory and Group Representations in Quantum Theory

Peter Woit

Masahito Hayashi

正人 林

N. V. Borisov

Peter Woit

Fl. Stancu

Abstract In quantum mechanics we are interested in the properties of eigenstates under various transformations (Chapter 1 ). Group theory offers a systematic way of finding these properties from the symmetries of the Hamiltonian. The eigenstates form linear vector spaces which in terms of group theory provide matrix representations of the group of transformationsG under consideration. Let us denote byD(g) such a representation where g is an element ofG.