Titlebook: Mathematical Concepts of Quantum Mechanics; Stephen J. Gustafson,Israel Michael Sigal Textbook 2020Latest edition Springer-Verlag GmbH Ger

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Dynamics,The purpose of this chapter is to investigate the existence and a key property – conservation of probability – of solutions of the Schrödinger equation for a particle of mass . in a potential .. The relevant background material on linear operators is reviewed in the Mathematical Supplement Chapter 25.

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Bound States and Variational Principle,In this chapter we develop powerful techniques for proving existence of bound states (eigenfunctions) corresponding to isolated eigenvalues. We also give estimates of their number.

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Existence of Atoms and Molecules,In this chapter we prove existence of stationary, well localized and stable states of atoms and, in a certain approximation, molecules. These are the lowest energy states, and their existence means that our quantum systems exist as well-localized objects, and do not disintegrate into fragments under sufficiently small perturbations.

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,Born–Oppenheimer Approximation and Adiabatic Dynamics,In this chapter, we discuss the Born–Oppenheimer approximation of molecular physics. This approximation lies at the foundation of quantum chemistry. It gave rise to adiabatic theory (see Sect. 12.5) in quantum mechanics and to multiscale analysis in mathematics and physics.

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Open Quantum Systems,In this chapter, we introduce and study the notion of open quantum system, generalizing that of the quantum system we have dealt with so far. This notion lies at the foundation of quantum information theory.