Review of the quantum mechanics of N-electron systems

Carsten A. Ullrich, Adam Wasserman

Abstract This chapter contains a review of quantum mechanics of one-electron systems, suitable for undergraduate students with a limited background of modern physics. It is first explained that matter consists of electrons and nuclei, and the concept of wave functions is introduced. The Schrödinger equation is then presented, and it is shown how the static Schrödinger equation emerges from the stationary limit of the time-dependent Schrödinger equation. Two examples are discussed: the particle in a box and plane waves. The chapter finishes by listing important concepts and properties of quantum mechanics, such as probability density, normalization, observables, operators, energy spectra, and orthonormal sets.

David O Hayward

Y. Imry

We start by reviewing some interesting results in mesoscopic physics illustrating nontrivial insights on Quantum Mechanics. We then review the general principles of dephasing (sometimes called “decoherence”) of Quantum-Mechanical interference by coupling to the environment degrees of freedom. A particular recent example of dephasing by a current-carrying (nonequilibrium) system is then discussed in some detail. This system is itself a manifestly Quantum Mechanical one and this is another illustration of detection without the need for “classical observers” etc. We conclude by describing briefly a recent problem having to do with the orbital magnetic response of conduction electrons (another manifestly Quantum Mechanical property): The magnetic response of a normal layer (N) coating a superconducting cylinder (S). Some recent very intriguing experimental results on a giant paramagnetic component of this response are explained using special states in the normal layer. It is hoped that these discussions illustrate not only the vitality and interest of mesoscopic physics but also its extreme relevance to fundamental issues in Quantum Mechanics.

S. K. Lamoreaux

A review of the experimental tests of quantum mechanics is presented. Tests of the wave-particle duality of matter for atoms, electrons, and neutrons are discussed. Also covered are applications of neutron interferometry to a variety of quantum mechanics tests. Tests of the topological nature of quantum mechanics (Aharonov-Bohm effect, Aharonov-Casher effect, Berry’s phase, Aharonov-Anandan phase) are reviewed. Other topics reviewed include the experimental tests of the Bell inequality, nonlinear additions to the Schrödinger equation, the Pauli exclusion principle, the Zeno effect, and the uniqueness of ħ.