Quantum mechanics (Q1572661)

The volume represents a solid and high level basis for lecturing in a first year graduate course on quantum mechanics. It is self-contained, requires no previous background in the field, and provides future research workers with the tools required to solve real problems. The first half of the course emphasizes bound-state problems. It begins with the familiar approach via differential equations and coordinate representations. A discussion of the factorization method and ladder operators for solving the eigenvalue problem leads naturally to the modern algebraic approach. Part II of the course treats time-independent perturbation theory. The role of symmetry breaking in removing degeneracies is emphasized, but cases in which the first order perturbation does not lead to the proper symmetry-adapted basis are also treated. Part III of the lectures provides a detailed discussion of rotational symmetry and angular momentum, including the Wigner-Eckart theorem, and the matrix elements of the general rotation operator and of vector-coupled tensor operators in terms of angular momentum recoupling coefficients. It includes a Chapter on the SO(2,1) algebra of a stretched Coulomb basis that avoids the infinite sum and continuum contributions of conventional perturbation treatments. Part IV gives a first introduction to systems of identical particles, with emphasis on the two-electron atom and a chapter on variational techniques. The second half of the course deals chiefly with continuum problems. Part V focuses on scattering theory; here, the polarization of particle beams and the scattering of particles with spin are used to introduce density matrices and statistical distributions of states. Part VI provides a conventional introduction to time-dependent perturbation theory, including a chapter on magnetic resonance and an application of the sudden and adiabatic approximations in the reversal of magnetic fields. Part VII deals with atom-photon interactions and includes an expansion of the quantized radiation field in terms of the full set of vector spherical harmonics, leading to a detailed derivation of the general electric and magnetic multipole-transition matrix elements needed in applications to nuclear transitions, in particular. Part VIII is an introduction to relativistic quantum mechanics, and Part IX, an introduction to many-body theory using annihilation-creation operator formalism. The applications and assigned problems of these lectures are taken largely from the fields of atomic and molecular physics and from nuclear physics, with a few examples from other fields. The problems are often real problems, meant to be somewhat of a challenge, guiding and testing the reader's understanding. They are an integral part of the course and are not assigned to specific chapters, but numbered within the two halves of the volume (1-55 resp. 1-51). Detailed solutions for certain key problems are given in the text of the lectures. More than 100 illustrations are included, and a comprehensive index of notions is provided. References to specific books or research articles are given throughout the lectures wherever they are particularly useful or relevant. The volume can be used by students without previous knowledge of quantum mechanics and by researchers in the field; it represents a beneficial investment for libraries and individuals as well.