Concepts, Methods and Applications of Quantum Systems in Chemistry and Physics

Alia Tadjer, Rossen L. Pavlov, J. Maruani +2 more

Sourav Pal, Vipin Srivastava, Vidya Avasare +1 more

Donald D. Fitts

This text presents a rigorous mathematical account of the principles of quantum mechanics, in particular as applied to chemistry and chemical physics. Applications are used as illustrations of the basic theory. The first two chapters serve as an introduction to quantum theory, although it is assumed that the reader has been exposed to elementary quantum mechanics as part of an undergraduate physical chemistry or atomic physics course. Following a discussion of wave motion leading to Schrödinger's wave mechanics, the postulates of quantum mechanics are presented along with essential mathematical concepts and techniques. The postulates are rigorously applied to the harmonic oscillator, angular momentum, the hydrogen atom, the variation method, perturbation theory, and nuclear motion. Modern theoretical concepts such as hermitian operators, Hilbert space, Dirac notation, and ladder operators are introduced and used throughout. This text is appropriate for beginning graduate students in chemistry, chemical physics, molecular physics and materials science.

Szilárd Szalay, Max J. Pfeffer, V. Murg +4 more

The treatment of high‐dimensional problems such as the Schrödinger equation can be approached by concepts of tensor product approximation. We present general techniques that can be used for the treatment of high‐dimensional optimization tasks and time‐dependent equations, and connect them to concepts already used in many‐body quantum physics. Based on achievements from the past decade, entanglement‐based methods—developed from different perspectives for different purposes in distinct communities already matured to provide a variety of tools—can be combined to attack highly challenging problems in quantum chemistry. The aim of the present paper is to give a pedagogical introduction to the theoretical background of this novel field and demonstrate the underlying benefits through numerical applications on a text book example. Among the various optimization tasks, we will discuss only those which are connected to a controlled manipulation of the entanglement which is in fact the key ingredient of the methods considered in the paper. The selected topics will be covered according to a series of lectures given on the topic “New wavefunction methods and entanglement optimizations in quantum chemistry” at the Workshop on Theoretical Chemistry, February 18–21, 2014, Mariapfarr, Austria. © 2015 Wiley Periodicals, Inc.