Elements of Quantum Mechanics and the H Atom

If the reader is already familiar with quantum mechanics he may just want to browse this chapter and return later if necessary. However, readers who have experienced quantum mechanics up to now only as compulsory mathematical exercise may perhaps read this chapter with advantage and find it helpful to approach the indispensable instruments without big formal hurdles. In Sects. 2.1–2.3 we summarize a minimum of formalism. Section 2.4 treats as a first example the well known particle in a box and the free electron gas which in atomic and solid state physics is an important elementary model. Section 2.5 gives an overview of how to treat angular momenta, needed in all following text, specified in Sect. 2.5.4 for the electron spin s=1/2. Section 2.6 offers a ‘crash course’ in nonrelativistic quantum mechanics of the H atom – essential knowledge for all the following chapters. We refrain here from formal derivations in favour of a plausible, possibly somewhat hand waving introduction. Finally, Sect. 2.7 presents a first, elementary approach to interactions of atomic electrons with external fields, which will be extended and deepened in Chap. 8. Clearly, such a brief introduction into quantum mechanics cannot substitute a profound study of the formal theory. It should, however, facilitate the access to it and make the reader ‘fit’ for the following chapters.