Group Theory The Application to Quantum Mechanics

Many books explore group theorys connection with physics, but few of them offer an introductory approach. This text provides upperlevel undergraduate and graduate students with a foundation in problem solving by means of eigenfunction transformation properties. This study focuses on eigenvalue problems in which differential equations or boundaries are unaffected by certain rotations or translations. Its explanation of transformations induced in function space by rotations (or translations) in configuration space has numerous practical applications — not only to quantum mechanics but also to anyother eigenvalue problems, including those of vibrating systems (molecules or lattices) or waveguides. Points of special interest include the development of Schur's lemma, which features a proof illustrated with a symbolic diagram. The text places particular emphasis on the geometric representation of ideas: for instance, the similarity transformation is characterized as a rotation in multidimensional function space and the reduction is described in terms of mutual orthogonal spaces. General references provide suggestions for further study, citing works of particular clarity and readability. New Preface to the Dover Edition. Problems. List of Symbols. References Cited. Systematic Bibliography. 1965 edition.

2. The Principles of Quantum Mechanics

3. Group Theory

4. General Applications to Quantum Mechanics; Wigners Theorem

5. Rotations in 3-Dimensional Space: Group D3

6. Continuation of the Theory of the Rotation Group

7. Space Groups

8. Finite Groups

Bibliography