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Nonrelativistic quantum mechanics. 3rd ed. (English) Zbl 1007.81002

Singapore: World Scientific. xvii, 522 p. (2002).
This book is a very clear and pleasant introduction to quantum mechanics.
It starts by describing experiments highlighting the need for quantum mechanics. After a quick introduction to classical mechanics, one goes on starting with Schrödinger’s equation and the associated wave interpretation. Chapter four and five focus on the one-dimensional case with two situations: scattering and bound states. Tunneling and the harmonic oscillator are introduced. Chapter six and seven present respectively the basics on Hilbert spaces and how this mathematical machinery is adapted to physical quantities. Chapter eight continues in the spirit of chapter six with a short review of distributions and Fourier transforms. Chapter nine studies the harmonic oscillator and “the rigid rotator” leading to the quantum mechanical characterization of angular momentum and to spin. Chapter ten is devoted to central force problems (invariant under rotations). The symmetry is used for simplifying the search for solutions to Schrödinger’s equation (angular variables can be discarded). For several potentials one gets solutions in various coordinate systems. Chapter eleven shows how transformations in abstract spaces lead to various “pictures” (Heisenberg, Schrödinger, Dirac) which are discussed next. Chapter twelve deals with solving the Schrödinger equation in complicated cases via a stationary perturbation. In the next chapter the degenerate case is studied. Optimization-based approaches are discussed subsequently and in chapter fifteen with time-dependent perturbations, transition rates will be relevant. The next two chapters apply the previous methods to the physical situation of a particle in a magnetic or electromagnetic field (Zeeman effect). In chapter eighteen and nineteen devoted to scattering theory, part of the energy spectrum is continuous. The last two chapters shift the focus to systems of particles in a quantum mechanical context and to quantum statistical mechanics. One finds an index and exercices with references at the end of each chapter.
This book can be recommended for teaching an introductory course in quantum mechanics.

MSC:

81-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81Q15 Perturbation theories for operators and differential equations in quantum theory
47A70 (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces
47N50 Applications of operator theory in the physical sciences
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
81U05 \(2\)-body potential quantum scattering theory
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