Unexpected properties of a quantum mechanical system

Paull Nunez

Peter Joshua Atkins, R. George Ratcliffe, Mark R. Wormald +1 more

This chapter pays particular attention to the quantum mechanics of motion. It is not possible to explain the structures and properties of atoms and molecules, where the role of electrons is central, without using quantum mechanics. Many of the processes of biochemistry involve the transfer of electrons and protons from a donor to an acceptor, and this migration can be understood only in terms of quantum theory. Here, the chapter introduces three fundamental types of motion — translation, rotation, and vibration — along with their characteristic quantum mechanical behaviours. It shows how various unexpected properties emerge, such as the ability of particles to penetrate into classically forbidden regions, the quantization of energy and angular momentum, and the existence of energy that cannot be removed from the system.

David W. Snoke

This chapter presents some basic calculations that show counterintuitive or unexpected results. First, it is shown that the Planck spectrum of light, which played an important role in the history of quantum mechanics, doesn’t say anything about the existence of indivisible particles. Second, a brief discussion of “chaos theory” shows that jumpy and unpredictable behavior can occur in classical systems. Last, the concept of “entanglement” is introduced as a basic property of quantum systems.

Josef Honerkamp

Giovanni Costa

David Krejčiřı́k, Petr Siegl, Miloš Tater +1 more

We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT-symmetric quantum mechanics.